Visual models of identities

Question 1ExpertLevel 68

Two strips of areas (4x) and (4x) are removed from a large square and a corner of area (16) is added back. If the original square was (x^2), the resulting area equals what?

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

Question 2ExpertLevel 68

In a square of side (u+v), the areas (u^2+v^2) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?

A(uv)B(u+v)C(2uv)D(u^2-v^2)

Question 3ExpertLevel 68

In a rectangle model, the length is (2x+3) and the width is (2x-3). Which area identity does it show?

A(4x^2+12x+9)B(4x^2-9)C(2x^2-9)D(4x^2-12x+9)

Question 4ExpertLevel 68

In a square tile model, the central square is (9a^2), the combined area of two equal strips is (30ab), and the small square is (25b^2). What is the side of the whole square?

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

Question 5ExpertLevel 68

In a model, strips of total area (14x) are added on two sides of an (x^2) square. How much corner area must be added to complete the square?

A(49)B(14)C(7x)D(196)

Question 6ExpertLevel 68

Which visual arrangement best forms the square model for (y^2-6y+9)?

ARemoving two (3y) strips from a square of side (y) and adding the (9) cornerBAdding two (3y) strips and a (9) corner to a square of side (y)CRemoving only (9) from a square of side (y)DAdding two separate squares (y^2) and (9)

Question 7ExpertLevel 68

In a rectangle model, (x^2+13x+36) must be split into two linear parts. Which pair is correct?

A(4x) and (9x)B(6x) and (6x)C(3x) and (10x)D(2x) and (11x)

Question 8ExpertLevel 68

If the region (a^2-b^2) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?

A(a+b)B(b-a)C(a-b)D(ab)

Question 9ExpertLevel 68

A model shows the difference between the areas of ((a+b)^2) and ((a-b)^2). What will this difference equal?

A(2ab)B(4ab)C(a^2+b^2)D(a^2-b^2)

Question 10ExpertLevel 68

A square model is to show ((2x+5)^2). What will be the areas of the four parts?

A(4x^2), (10x), (10x), (25)B(2x^2), (5x), (5x), (25)C(4x^2), (20x), (20x), (25)D(4x^2), (10x), (25x), (25)

Question 11ExpertLevel 68

In a visual model of an algebraic identity, a large square is divided into one small square, two congruent rectangles, and another small square. Which identity does it represent?

A(a+b)^2=a^2+2ab+b^2B(a-b)^2=a^2-2ab+b^2C(a+b)(a-b)=a^2-b^2Da^2+b^2=(a+b)^2

Question 12ExpertLevel 68

In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?

A(a^2+b^2)B(a^2+2ab+b^2)C(a^2-b^2)D(2a+2b)

Question 13ExpertLevel 68

In the model of (x^2+2xy+y^2), if (y) is drawn very small, which conclusion still remains correct?

AThe identity is true only for large (y)BThe two (xy) rectangles still existCThe (y^2) area disappearsDThe total area becomes (x^2+xy)

Question 14ExpertLevel 68

A rectangle is divided into parts (x^2), (5x), (7x), and (35). What are the possible sides of the rectangle?

A(x+12) and (x+35)B(x+5) and (x+7)C(x-5) and (x-7)D(x+1) and (x+35)

Question 15ExpertLevel 68

A square model has area (16p^2-40pq+25q^2). It represents a square with which side?

A(4p+5q)B(16p-25q)C(4p-5q)D(8p-10q)

Question 16ExpertLevel 68

A visual model compares (a^2+2ab+b^2) with (a^2+b^2). Which area belongs only to the cross rectangles?

A(a^2+b^2)B(ab)C(2ab)D(a+b)

Question 17ExpertLevel 68

If the tile model of (x^2+9x+20) forms a complete rectangle, which arrangement is correct?

ASides (x+4) and (x+5)BSides (x+2) and (x+10)CSides (x+9) and (x+20)DSides (x+1) and (x+20)

Question 18ExpertLevel 68

In a square model for ((3x-2y)^2), what will be the combined area of the two removed strips?

A(6xy)B(12xy)C(4y^2)D(9x^2)

Question 19ExpertLevel 68

Which model gives the most direct visual explanation of ((a+b)(a-b)=a^2-b^2)?

ARemoving a square of side (b) from a square of side (a) and rearranging the remainder into a rectangleBMaking four equal triangles in a square of side (a+b)CAdding two separate squares (a^2) and (b^2)DAdding (b^2) to a square of side (a-b)

Question 20ExpertLevel 68

In a model, (x^2+2xk+k^2) is a perfect square. If the total area of the linear strips is (16x), what is the corner area?

A(16)B(64)C(8)D(256)

Visual models of identities

Quiz this set

Two strips of areas (4x) and (4x) are removed from a large square and a corner of area (16) is added back. If the original square was (x^2), the resulting area equals what?

In a square of side (u+v), the areas (u^2+v^2) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?

In a rectangle model, the length is (2x+3) and the width is (2x-3). Which area identity does it show?

In a square tile model, the central square is (9a^2), the combined area of two equal strips is (30ab), and the small square is (25b^2). What is the side of the whole square?

In a model, strips of total area (14x) are added on two sides of an (x^2) square. How much corner area must be added to complete the square?

Which visual arrangement best forms the square model for (y^2-6y+9)?

In a rectangle model, (x^2+13x+36) must be split into two linear parts. Which pair is correct?

If the region (a^2-b^2) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?

A model shows the difference between the areas of ((a+b)^2) and ((a-b)^2). What will this difference equal?

A square model is to show ((2x+5)^2). What will be the areas of the four parts?

In a visual model of an algebraic identity, a large square is divided into one small square, two congruent rectangles, and another small square. Which identity does it represent?

In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?

In the model of (x^2+2xy+y^2), if (y) is drawn very small, which conclusion still remains correct?

A rectangle is divided into parts (x^2), (5x), (7x), and (35). What are the possible sides of the rectangle?

A square model has area (16p^2-40pq+25q^2). It represents a square with which side?

A visual model compares (a^2+2ab+b^2) with (a^2+b^2). Which area belongs only to the cross rectangles?

If the tile model of (x^2+9x+20) forms a complete rectangle, which arrangement is correct?

In a square model for ((3x-2y)^2), what will be the combined area of the two removed strips?

Which model gives the most direct visual explanation of ((a+b)(a-b)=a^2-b^2)?

In a model, (x^2+2xk+k^2) is a perfect square. If the total area of the linear strips is (16x), what is the corner area?

Quiz result

Visual models of identities

Quiz this set

Two strips of areas (4x) and (4x) are removed from a large square and a corner of area (16) is added back. If the original square was (x^2), the resulting area equals what?

In a square of side (u+v), the areas (u^2+v^2) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?

In a rectangle model, the length is (2x+3) and the width is (2x-3). Which area identity does it show?

In a square tile model, the central square is (9a^2), the combined area of two equal strips is (30ab), and the small square is (25b^2). What is the side of the whole square?

In a model, strips of total area (14x) are added on two sides of an (x^2) square. How much corner area must be added to complete the square?

Which visual arrangement best forms the square model for (y^2-6y+9)?

In a rectangle model, (x^2+13x+36) must be split into two linear parts. Which pair is correct?

If the region (a^2-b^2) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?

A model shows the difference between the areas of ((a+b)^2) and ((a-b)^2). What will this difference equal?

A square model is to show ((2x+5)^2). What will be the areas of the four parts?

In a visual model of an algebraic identity, a large square is divided into one small square, two congruent rectangles, and another small square. Which identity does it represent?

In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?

In the model of (x^2+2xy+y^2), if (y) is drawn very small, which conclusion still remains correct?

A rectangle is divided into parts (x^2), (5x), (7x), and (35). What are the possible sides of the rectangle?

A square model has area (16p^2-40pq+25q^2). It represents a square with which side?

A visual model compares (a^2+2ab+b^2) with (a^2+b^2). Which area belongs only to the cross rectangles?

If the tile model of (x^2+9x+20) forms a complete rectangle, which arrangement is correct?

In a square model for ((3x-2y)^2), what will be the combined area of the two removed strips?

Which model gives the most direct visual explanation of ((a+b)(a-b)=a^2-b^2)?

In a model, (x^2+2xk+k^2) is a perfect square. If the total area of the linear strips is (16x), what is the corner area?

Quiz result

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