Which figure directly shows the area ((u-v)^2)?
Correct answer: A
The area of a square equals the square of its side. Exam tip: connect ((u-v)^2) with a subtraction square.
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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Easy · Level 72 · square-area,minus-binomial,visual-model
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- Square with side (u-v)
- Square with side (u+v)
- Rectangle with dimensions (u+v) and (u-v)
- Square with side (v)
Easy · Level 72 · complete-square,small-square,area-tiles
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- (12)
- (36)
- (6)
- (3)
Easy · Level 72 · conjugate-model,cancellation,difference-identity
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- Because they are equal and have opposite signs
- Because (r^2) is zero
- Because (s^2) is added
- Because both sides are equal
Easy · Level 72 · distributive-law,rectangle-area,visual-algebra
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- (x^2+9)
- (9x^2+x)
- (x^2+9x)
- (x+9)
Easy · Level 72 · coefficient-square,area-model,binomial-expansion
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- (4x^2+4x+1)
- (2x^2+4x+1)
- (4x^2+2x+1)
- (4x^2+1)
Easy · Level 72 · algebraic identities,visual models,binomial square,area model,class 9 mathematics
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- \((x+y)^2\)
- \((x-y)^2\)
- \(x^2-y^2\)
- \(x^2+y^2\)
Easy · Level 72 · small-square,minus-square,visual-identity
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- (5x)
- (10x)
- (25)
- (x^2)
Easy · Level 72 · four-parts,square-model,visual-proof
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- Square with side (a+b)
- Square with side (a-b)
- Rectangle with dimensions (a+b) and (a-b)
- Square with side (ab)
Easy · Level 72 · factor-model,rectangle-tiles,dimensions
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- (x+9) and (x+20)
- (x+4) and (x+5)
- (x+2) and (x+10)
- (x+1) and (x+20)
Easy · Level 72 · common-error,visual-model,binomial-square
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- Two (3x) rectangles
- One (9x) rectangle
- Two (x^2) squares
- One (x+3) line
Easy · Level 72 · visual-proof,same-area,square-identity
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- (a^2-b^2=(a+b)(a-b))
- (a(a+b)=a^2+ab)
- (a^2+2ab+b^2=(a+b)^2)
- (a^2-b^2=(a-b)^2)
Easy · Level 72 · algebraic identities, square of difference, area of square, visual models, class 9 mathematics
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- 48
- 63
- 64
- 49
Easy · Level 72 · common-factor,rectangle-model,area
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- Rectangle with length (a+b) and breadth (a)
- Square with side (a+b)
- Rectangle with length (a-b) and breadth (b)
- Square with side (ab)
Easy · Level 72 · conjugate-product,difference-of-squares,visual-model
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- (x^2+16)
- (x^2-8x+16)
- (x^2-16)
- (x^2+8x+16)
Easy · Level 72 · small-square,coefficient-model,visual-identity
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- (2)
- (4)
- (6x)
- \(9x^2\)
Easy · Level 72 · minus-square,side-recognition,visual-model
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- (x+5)
- (x-10)
- (x-5)
- (x+25)
Easy · Level 72 · numeric-difference,rectangle-model,visual-identity
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- (6+2) and (6-2)
- (6) and (2)
- (6+6) and (2+2)
- (6-2) and (6-2)
Easy · Level 72 · algebraic identities,visual models,area model,binomial square,class 9 mathematics
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- A square of side \(a+b\) is divided into \(a^2\), \(b^2\), and two rectangles of area \(ab\).
- The model consists of only one rectangle with sides \(a\) and \(b\).
- A square of side \(a-b\) is divided into four equal parts.
- The model is formed by a triangle with base \(a+b\) and height \(a+b\).
Easy · Level 72 · three-term-square,pair-rectangles,visual-counting
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- Once
- Twice
- Thrice
- Six times
Easy · Level 72 · perfect-square,outer-side,area-tiles
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- (x+16)
- (x+4)
- (x+8)
- (x-8)
If (x^2+12x+36) is read through a complete square model, what is the side of the small square?
Correct answer: C
The small square has area (36), so its side is (6). Exam tip: take the square root of the last term.
View question detailsIn the visual model of ((r+s)(r-s)), why do the middle terms not remain?
Correct answer: A
One term is (rs) and the other is (-rs), so they cancel. Exam tip: watch the middle terms in conjugate multiplication.
View question detailsWhat is the area of (x(x+9)) in the rectangle model?
Correct answer: C
Splitting the rectangle into (x) and (9) parts gives (x^2) and (9x). Exam tip: understand the distributive law through area.
View question detailsWhat is the total area in the visual model of a square with side (2x+1)?
Correct answer: A
The square of (2x) is (4x^2), and the two rectangles have total area (4x). Exam tip: do not forget to square the coefficient.
View question detailsWhich algebraic expression has a visual model of one large square containing a square of area \(x^2\), a square of area \(y^2\), and two equal rectangles of area \(xy\)?
Correct answer: A
The large square has side \(x+y\). Its parts have total area \(x^2+xy+xy+y^2=x^2+2xy+y^2\), so it represents \((x+y)^2\). Exam tip: two \(xy\) rectangles always contribute the middle term \(2xy\).
View question detailsIn the model of a square with side (x-5), what will be the area of the final small square?
Correct answer: C
The small square has side (5), so its area is (25). Exam tip: the square of the negative part is positive.
View question detailsIn which visual model are the four area parts of (a^2+2ab+b^2) clearly visible?
Correct answer: A
A square of side (a+b) splits into (a^2), (ab), (ab), and (b^2). Exam tip: add the four parts to form the identity.
View question detailsIf a rectangle model has parts (x^2), (4x), (5x), and (20), what can the outer dimensions be?
Correct answer: B
The numbers (4) and (5) make (4x), (5x), and (20). Exam tip: the corner area is the product of numerical parts.
View question detailsA student writes ((x+3)^2) as (x^2+9). According to the visual model, what is missing?
Correct answer: A
A complete square has two (3x) rectangles along with (x^2) and (9). Exam tip: do not omit the middle term (6x).
View question detailsWhich identity is proved by equating the area of a square with side (a+b) and the sum of its inner parts?
Correct answer: C
The same square has outside area ((a+b)^2) and inside area (a^2+2ab+b^2). Exam tip: remember two forms of the same area.
View question detailsUsing identity, what is the area of a square with side (8-1)?
Correct answer: D
The area of a square is the square of its side. Here the side is \((8-1)\), so the area is \((8-1)^2\). Using \((a-b)^2=a^2-2ab+b^2\), we get \(8^2-2\times8\times1+1^2=64-16+1=49\). Option 64 is only \(8^2\), so it ignores the effect of subtracting 1. Exam tip: always include the middle term \(-2ab\) while expanding \((a-b)^2\).
View question detailsWhich visual model shows (a(a+b)) by combining one (a^2) square and one (ab) rectangle?
Correct answer: A
The rectangle area is (a(a+b)), and the sum of parts is (a^2+ab). Exam tip: identify the common factor from the figure.
View question detailsIf ((x+4)(x-4)) is viewed through a rectangle model, what will the area be?
Correct answer: C
This is a conjugate product, and the middle terms cancel. Exam tip: identify ((a+b)(a-b)=a^2-b^2).
View question detailsIn a square with side (3x+2), what will be the area of the small square?
Correct answer: B
The small square has side (2), so its area is \(2^2=4\). Exam tip: square the constant part.
View question detailsIn a visual model, (x^2-10x+25) shows the side of which square?
Correct answer: C
Since (25=5^2) and (-10x=-2\times x\times5), the side is (x-5). Exam tip: look at the negative middle term.
View question detailsIf (6^2-2^2) is changed into a visual rectangle, what will the dimensions be?
Correct answer: A
In difference of squares, the dimensions become ((a+b)) and ((a-b)). Exam tip: compute (6^2-2^2=8\times4).
View question detailsWhich partition is correct in the area model of the algebraic identity \((a+b)^2\)?
Correct answer: A
Dividing a square of side \(a+b\) at lengths \(a\) and \(b\) gives areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Their sum is \(a^2+2ab+b^2\). Exam tip: always count both \(ab\) rectangles.
View question detailsIn the visual model of a square with side (a+b+c), how many times will the (bc) rectangle appear?
Correct answer: B
Each different pair forms two equal rectangles, so (bc) appears twice. Exam tip: count paired rectangles.
View question detailsIf (x^2+16x+64) is a complete square model, what is the outer side?
Correct answer: C
Since (64=8^2) and (16x=2\times8\times x), the side is (x+8). Exam tip: check using the square root of the last term.
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