Visual models of identities

Question 1HardLevel 67

In a visual proof, the same large square area is written as ((a+b)^2) and (a^2+2ab+b^2). What is the conclusion?

ABoth areas are equalBThe first area is always greaterCThe second area is always zeroDThey are areas of different figures

Question 2HardLevel 67

If (x^2-6x+9) is read through a visual model, which square is formed?

ASquare with side (x+3)BSquare with side (x-3)CSquare with side (x-6)DSquare with side (x+9)

Question 3HardLevel 67

In which visual model is the small square actually (6) by (6) to complete (x^2+12x+36)?

AModel of a square with side (x+6)BModel of a square with side (x+12)CRectangle with dimensions (x+3) and (x+9)DRectangle with dimensions (x-6) and (x+6)

Question 4HardLevel 67

In a model, the remaining area (x^2-25) is shown by the rectangle ((x+5)(x-5)). If (x=12), what is the area of the visual rectangle?

A(119)B(144)C(169)D(100)

Question 5HardLevel 67

If in a square model the (36) corner is added with an (x^2) tile but without adding two equal rectangles, why will a complete square not form?

ABecause the two middle (6x) rectangles are missingBBecause (36) is not a squareCBecause (x^2) is not an areaDBecause (x) is always (6)

Question 6HardLevel 67

In the rectangle model of ((x-3)(x-7)), what will the constant corner be like?

APositive (21)BNegative (21)CPositive (10x)DNegative (10x)

Question 7HardLevel 67

If the area model of (25a^2-30ab+9b^2) is a square, what will be its side?

A(5a+3b)B(25a-9b)C(5a-3b)D(10a-6b)

Question 8HardLevel 67

In the visual model of ((a+b+c)^2), how many rectangular cross parts are there in total?

A(3)B(4)C(5)D(6)

Question 9HardLevel 67

In which rectangle model can the parts of (x^2+x-12) be formed?

A((x+4)(x-3))B((x-4)(x-3))C((x+6)(x-2))D((x+12)(x-1))

Question 10HardLevel 67

If (6x) and (10x) are two cross rectangles and the corner is (15), what can be the outer dimensions of the rectangle?

A(2x+5) and (3x+3)B(2x+3) and (3x+5)C(6x+10) and (x+15)D(x+6) and (x+10)

Question 11HardLevel 67

In a visual model, the rectangle for (x^2+14x+40) must be divided into two numerical parts. Which parts are correct?

A(4) and (10)B(5) and (9)C(2) and (20)D(6) and (8)

Question 12HardLevel 67

If the outer dimensions in a rectangle model are (x-5) and (x+9), what will be the total area of the (x)-rectangles?

A(14x)B(4x)C(-4x)D(-45x)

Question 13HardLevel 67

A square model shows (64x^2-80xy+25y^2). It is the area of a square with which side?

A(8x+5y)B(64x-25y)C(8x-5y)D(16x-10y)

Question 14HardLevel 67

In which visual situation can ((x+4)^2-(x-4)^2) be understood as the difference of areas of two squares?

ATwo squares with sides (x+4) and (x-4)BOne rectangle with only side (x+4)CTwo equal squares with side (x)DOne circle and one square

Question 15HardLevel 67

If ((x+4)^2-(x-4)^2) is transformed using difference of squares, what will the area equal?

A(8x)B(16x)C(x^2-16)D(x^2+16)

Question 16HardLevel 67

If a square with side (x+a) has a small square of area (a^2), what will be the total area of the two rectangles?

A(ax)B(2ax)C(x^2+a^2)D(2a^2x)

Question 17HardLevel 67

In the visual models of ((2x+3y)^2) and ((2x-3y)^2), which part changes sign?

A(4x^2)B(9y^2)CMiddle term (12xy)DBoth square terms

Question 18HardLevel 67

If an area model shows (36x^2-1), which rectangle will be formed by difference of squares?

A((6x+1)(6x-1))B((36x+1)(36x-1))C((6x+1)(x-1))D((18x+1)(18x-1))

Question 19HardLevel 67

A student writes only (x^2+4) for the model of ( (x+2)^2 ). Based on the visual model, what is the mistake?

AThe student counted (x^2) twiceBThe student omitted two (2x) rectanglesCThe student made (4) negativeDThe student took side (x-2)

Question 20HardLevel 67

Which visual comparison explains the meaning of ( (x+5)^2-(x^2+25) )?

AOnly the area of two (5x) rectangles remains from the complete squareB(x^2) also remains from the complete squareCThe square (25) remains from the complete squareDNo area remains

Visual models of identities

Quiz this set

In a visual proof, the same large square area is written as ((a+b)^2) and (a^2+2ab+b^2). What is the conclusion?

If (x^2-6x+9) is read through a visual model, which square is formed?

In which visual model is the small square actually (6) by (6) to complete (x^2+12x+36)?

In a model, the remaining area (x^2-25) is shown by the rectangle ((x+5)(x-5)). If (x=12), what is the area of the visual rectangle?

If in a square model the (36) corner is added with an (x^2) tile but without adding two equal rectangles, why will a complete square not form?

In the rectangle model of ((x-3)(x-7)), what will the constant corner be like?

If the area model of (25a^2-30ab+9b^2) is a square, what will be its side?

In the visual model of ((a+b+c)^2), how many rectangular cross parts are there in total?

In which rectangle model can the parts of (x^2+x-12) be formed?

If (6x) and (10x) are two cross rectangles and the corner is (15), what can be the outer dimensions of the rectangle?

In a visual model, the rectangle for (x^2+14x+40) must be divided into two numerical parts. Which parts are correct?

If the outer dimensions in a rectangle model are (x-5) and (x+9), what will be the total area of the (x)-rectangles?

A square model shows (64x^2-80xy+25y^2). It is the area of a square with which side?

In which visual situation can ((x+4)^2-(x-4)^2) be understood as the difference of areas of two squares?

If ((x+4)^2-(x-4)^2) is transformed using difference of squares, what will the area equal?

If a square with side (x+a) has a small square of area (a^2), what will be the total area of the two rectangles?

In the visual models of ((2x+3y)^2) and ((2x-3y)^2), which part changes sign?

If an area model shows (36x^2-1), which rectangle will be formed by difference of squares?

A student writes only (x^2+4) for the model of ( (x+2)^2 ). Based on the visual model, what is the mistake?

Which visual comparison explains the meaning of ( (x+5)^2-(x^2+25) )?

Quiz result

Visual models of identities

Quiz this set

In a visual proof, the same large square area is written as ((a+b)^2) and (a^2+2ab+b^2). What is the conclusion?

If (x^2-6x+9) is read through a visual model, which square is formed?

In which visual model is the small square actually (6) by (6) to complete (x^2+12x+36)?

In a model, the remaining area (x^2-25) is shown by the rectangle ((x+5)(x-5)). If (x=12), what is the area of the visual rectangle?

If in a square model the (36) corner is added with an (x^2) tile but without adding two equal rectangles, why will a complete square not form?

In the rectangle model of ((x-3)(x-7)), what will the constant corner be like?

If the area model of (25a^2-30ab+9b^2) is a square, what will be its side?

In the visual model of ((a+b+c)^2), how many rectangular cross parts are there in total?

In which rectangle model can the parts of (x^2+x-12) be formed?

If (6x) and (10x) are two cross rectangles and the corner is (15), what can be the outer dimensions of the rectangle?

In a visual model, the rectangle for (x^2+14x+40) must be divided into two numerical parts. Which parts are correct?

If the outer dimensions in a rectangle model are (x-5) and (x+9), what will be the total area of the (x)-rectangles?

A square model shows (64x^2-80xy+25y^2). It is the area of a square with which side?

In which visual situation can ((x+4)^2-(x-4)^2) be understood as the difference of areas of two squares?

If ((x+4)^2-(x-4)^2) is transformed using difference of squares, what will the area equal?

If a square with side (x+a) has a small square of area (a^2), what will be the total area of the two rectangles?

In the visual models of ((2x+3y)^2) and ((2x-3y)^2), which part changes sign?

If an area model shows (36x^2-1), which rectangle will be formed by difference of squares?

A student writes only (x^2+4) for the model of ( (x+2)^2 ). Based on the visual model, what is the mistake?

Which visual comparison explains the meaning of ( (x+5)^2-(x^2+25) )?

Quiz result

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