In the area model of a square with side (x+3), what will be the four parts?
Correct answer: A
Two rectangles (3x) and (3x) are formed and the small corner is (9). In exams split the square model into four parts.
View question detailsMathematics
Visual models of identities
सर्वसमिकाओं के दृश्य मॉडल
In Class 9 Mathematics, under the chapter Exploring Algebraic Identities, students use geometric diagrams and area-based representations to understand algebraic identities visually. They relate squares and rectangles formed from algebraic expressions to expansions such as binomial products, helping them see why both sides of an identity are equal rather than merely memorising formulas.
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Medium · Level 68 · visual model,area model,binomial square
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- (x^2), (3x), (3x), (9) / correct parts
- (x^2), (6x), (9), (9) / repeated corner
- (x^2), (3x), (9), (12) / mixed parts
- (x^2), (x), (3x), (9) / wrong strip
Medium · Level 68 · perfect square,visual model,side length
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- (y+8) / middle coefficient used
- (y+4) / correct side
- (y-4) / wrong sign
- (y+16) / corner used as side
Medium · Level 68 · subtraction model,overlap,visual identity
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- (5a) / one removed strip
- (10a) / total removed strips
- (25) / overlap square
- (a^2) / main square
Medium · Level 68 · difference of squares,rectangle model,visual proof
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- (x^2+36) / sum of squares
- (x^2-12x+36) / square of difference
- (x^2+12x+36) / square of sum
- (x^2-36) / difference of squares
Medium · Level 68 · area model,added strips,binomial square
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- \(p^2+4p+4\) / complete area
- \(p^2+2p+4\) / one strip missing
- \(p^2+4p+2\) / corner not squared
- \(p^2-4p+4\) / subtraction model
Medium · Level 68 · visual partition,square model,algebraic identity
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- (m^2), (7m), (49) / one strip missing
- (m^2), (14m), (49), (49) / extra corner
- (m^2), (7m), (7m), (49) / correct partition
- (m^2), (49m), (49m), (7) / wrong parts
Medium · Level 68 · common error,subtraction model,visual identity
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- (8x) / unsigned middle
- (4x) / one strip
- (16x) / wrong product
- (-8x+32) / correction difference
Medium · Level 68 · rectangle model,factor tiles,area parts
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- sum based
- correct sides
- same product wrong strips
- wrong signs
Medium · Level 68 · main square,corner square,visual model
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- correct squares
- unsquared parts
- side products
- main part wrong
Medium · Level 68 · middle area,binomial square,visual model
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- (3x) / one rectangle
- (6x) / total middle area
- (9x^2) / main square
- (1) / corner square
Medium · Level 68 · difference of squares,cut model,visual identity
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- remove square of side (9) from square of side (z)
- form square of side (z+9)
- form square of side (z-9)
- form rectangle of sides (z) and (9)
Medium · Level 68 · equal rectangles,perfect square,area model
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- (12x) / total middle
- (36x) / corner product
- (6x) / each rectangle
- (x+6) / side length
Medium · Level 68 · constant corner,rectangle model,area grid
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- (11) / sum of constants
- (24) / product of constants
- (5) / difference of constants
- (3x+8x) / middle strips
Medium · Level 68 · perfect square,negative middle,visual model
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- square of side (2a+3)
- square of side (4a-9)
- square of side (2a-3)
- square of side (4a+3)
Medium · Level 68 · algebraic identities,visual models,area model,binomial square,perfect square,class 9 mathematics
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- \((a+b)^2=a^2+2ab+b^2\)
- \((a-b)^2=a^2-2ab+b^2\)
- \(a^2-b^2=(a+b)(a-b)\)
- \((a+b)^2=a^2+b^2\)
Medium · Level 68 · common mistake,missing strips,visual model
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- (4n) / one strip
- (8n) / two strips
- (16n) / corner times variable
- (n+4) / side length
Medium · Level 68 · grid model,rectangle area,visual multiplication
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- (x^2+7x+10) / correct total
- (x^2+10x+7) / swapped terms
- (x^2+5x+2) / corner missed
- (x^2-7x+10) / wrong sign
Medium · Level 68 · numerical identity,mental math,visual square
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- ((100-2)^2) / subtraction square model
- ((90+8)^2) / less direct sum model
- (100^2-2^2) / difference of squares only
- (98\cdot100) / rectangle only
Medium · Level 68 · subtraction model,removed strips,visual identity
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- (2x) / one strip
- (4x) / two strips
- (4) / overlap square
- (x^2-4) / remaining area
Medium · Level 68 · factor model,rectangle tiles,visual algebra
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- product only
- correct factors
- sum only
- wrong signs
If (y^2), (8y), and (16) make a perfect square in a model, what will be the outer side?
Correct answer: B
Since (16=4^2) and (2\cdot y\cdot4=8y), the side is (y+4). In exams take the square root of the last term.
View question detailsIn the subtraction model of a square with side (a-5), what is the final added corner?
Correct answer: C
When two (5a) strips are removed, the (5) by (5) corner is removed twice. In exams add back the overlap in a subtraction model.
View question detailsA rectangle has sides (x+6) and (x-6). What will be the area in the visual model?
Correct answer: D
The product of sum and difference gives (x^2-36). In exams use difference of squares when opposite signs appear.
View question detailsTwo strips of width (2) and a (2) by (2) corner are added to a (p) by (p) square. What is the new area?
Correct answer: A
The two strips give \(2p+2p=4p\) and the corner gives (4). In exams add all the added parts.
View question detailsWhich visual partition correctly shows ((m+7)^2)?
Correct answer: C
A square of side (m+7) has two equal (7m) strips and a (49) corner. In exams identify equal strips.
View question detailsA student wrote the model of ((x-4)^2) as (x^2-16). Which part was missed?
Correct answer: D
The correct expansion is (x^2-8x+16), so the difference from (x^2-16) is (-8x+32). In exams keep square of difference and difference of squares separate.
View question detailsIn a rectangle model, the parts are (x^2), (2x), (9x), and (18). What are the sides?
Correct answer: B
The strips (2x) and (9x) show the constant parts (2) and (9). In exams also check the corner product.
View question detailsIn the model of a square with side (2x+5), what are the main square and small corner respectively?
Correct answer: A
The main square is ((2x)^2=4x^2) and the corner is (5^2=25). In exams square both side parts separately.
View question detailsIf the visual model of ((3x+1)^2) is made, what is the total middle area?
Correct answer: B
The middle area is (2\cdot3x\cdot1=6x). In exams use (2ab) for the middle part of a perfect square.
View question detailsIn which model can (z^2-81) be shown by changing it into a rectangle?
Correct answer: A
Since (81=9^2), this is a model of removing a smaller square from a larger square. In exams understand difference of squares by cut and rearrange.
View question detailsIn the visual model, (x^2+12x+36) is a perfect square. What is the area of each equal rectangle?
Correct answer: C
The total middle area is (12x), so each of the two equal rectangles is (6x). In exams split the middle term into two equal parts.
View question detailsA rectangle has sides (x+3) and (x+8). What will be the constant corner in the area model?
Correct answer: B
The constant corner is (3\cdot8=24). In exams multiply both constant parts for the small corner.
View question detailsWhich model correctly shows (4a^2-12a+9) as a perfect square?
Correct answer: C
(4a^2=(2a)^2), (9=3^2), and the middle term is negative. In exams choose (+) or (-) by checking the sign.
View question detailsA square visual model is divided into four regions with areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Which algebraic identity does this model represent?
Correct answer: A
The total area of the four regions is \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Each side of the complete square is \(a+b\), so its area is \((a+b)^2\). Hence, the identity is \((a+b)^2=a^2+2ab+b^2\). Option B has the middle term \(-2ab\), which belongs to the square of a difference. Exam tip: combine the two \(ab\) rectangles to obtain \(2ab\).
View question detailsIn a square with side (n+4), only (n^2) and (16) are written. What total area is missing?
Correct answer: B
Two (4n) strips are missing, so the total missing area is (8n). In exams do not omit the middle term in ((n+4)^2).
View question detailsIn a grid model, the rows are (x) and (5), and the columns are (x) and (2). What will be the total area?
Correct answer: A
The four cells are (x^2), (2x), (5x), and (10), whose sum is (x^2+7x+10). In exams multiply every cell.
View question detailsWhich area model can show (98^2) easily?
Correct answer: A
Since (98=100-2), the subtraction square model gives quick calculation. In exams use the nearest round number.
View question detailsIn the model of a square with side (x-2), how much rectangular area is subtracted from (x^2) in total?
Correct answer: B
Two (2x) strips are removed, so the total removed rectangular area is (4x). In exams count both removed strips.
View question detailsIf a rectangle area model is (x^2+10x+21), which sides will be correct?
Correct answer: B
Since (3+7=10) and (3\cdot7=21), the sides are (x+3) and (x+7). In exams check both sum and product.
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