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Quadratic Expressions and Area

7.3.1 Quadratic Expressions and Area

7.3.1 • Quadratic Expressions and Area

Warm Up

Figure A is a large square. Figure B is a large square with a smaller square removed. Figure C is composed of two large squares with one smaller square added.

Figure A

A square.

Figure B

A square with a 1 by 1 square removed from the lower left interior.

Figure C

Two large squares connected on the right side to a one by one smaller square.

Write an expression to represent the area of each shaded figure when the side length of the large square is as shown in the first column.

Copy and complete the table. Compare your work by answering 1 - 12.

Side length of large square Area of A Area of B Area of C

4 4

x x

4 x 4 x

x + 3 x + 3

1.

When the side length of the large square is 4 4 , what is the area of figure A?

Compare your answer:

4 2 4 2 (or an equivalent expression)

2.

When the side length of the large square is 4 4 , what is the area of figure B?

Compare your answer:

4 2 − 1 4 2 − 1 (or an equivalent expression)

3.

When the side length of the large square is 4 4 , what is the area of figure C?

Compare your answer:

2 ( 4 2 ) + 1 2 ( 4 2 ) + 1 (or an equivalent expression)

4.

When the side length of the large square is x x , what is the area of figure A?

Compare your answer:

x 2 x 2 (or an equivalent expression)

5.

When the side length of the large square is x x , what is the area of figure B?

Compare your answer:

x 2 − 1 x 2 − 1 (or an equivalent expression)

6.

When the side length of the large square is x x , what is the area of figure C?

Compare your answer:

2 x 2 + 1 2 x 2 + 1 (or an equivalent expression)

7.

When the side length of the large square is 4 x 4 x , what is the area of figure A?

Compare your answer:

16 x 2 16 x 2 or ( 4 x ) 2 ( 4 x ) 2 (or an equivalent expression)

8.

When the side length of the large square is 4 x 4 x , what is the area of figure B?

Compare your answer:

16 x 2 − 1 16 x 2 − 1 (or an equivalent expression)

9.

When the side length of the large square is 4 x 4 x , what is the area of figure C?

Compare your answer:

32 x 2 + 1 32 x 2 + 1 (or an equivalent expression)

10.

When the side length of the large square is x + 3 x + 3 , what is the area of figure A?

Compare your answer:

( x + 3 ) 2 ( x + 3 ) 2 or ( x + 3 ) ( x + 3 ) ( x + 3 ) ( x + 3 ) (or an equivalent expression)

11.

When the side length of the large square is x + 3 x + 3 , what is the area of figure B?

Compare your answer:

( x + 3 ) 2 − 1 ( x + 3 ) 2 − 1 (or an equivalent expression)

12.

When the side length of the large square is x + 3 x + 3 , what is the area of figure C

Compare your answer:

2 ( x + 3 ) 2 + 1 2 ( x + 3 ) 2 + 1 (or an equivalent expression)