The L-shape is a square of side a with a square of side b removed from one corner, so its area is a² − b². Piece P is cut along the orange dashed line, turned and placed beside piece Q to form the rectangle on the right. What does the rectangle show a² − b² is equal to?

Question

Accepted Answer

(a + b)(a − b). Piece Q is a long and a - b tall. P turned is b wide and a - b tall, so the rectangle is (a + b) long and (a - b) tall. Hence a^2 - b^2 = (a + b)(a - b).

The L-shape is a square of side a with a square of side $b$ removed from one corner, so its area is $a^{2} - b^{2}$ . Piece P is cut along the orange dashed line, turned and placed beside piece Q to form the rectangle on the right. What does the rectangle show $a^{2} - b^{2}$ is equal to?

Step-by-Step Solution

Key idea: The three classic identities

Master this chapter in 30 minutes a day.

More Class 8 Algebraic Expressions and Identities practice

The L-shape is a square of side a with a square of side b removed from one corner, so its area is a2−b2. Piece P is cut along the orange dashed line, turned and placed beside piece Q to form the rectangle on the right. What does the rectangle show a2−b2 is equal to?

Step-by-Step Solution

Key idea: The three classic identities

Master this chapter in 30 minutes a day.

More Class 8 Algebraic Expressions and Identities practice

The L-shape is a square of side a with a square of side $b$ removed from one corner, so its area is $a^{2} - b^{2}$ . Piece P is cut along the orange dashed line, turned and placed beside piece Q to form the rectangle on the right. What does the rectangle show $a^{2} - b^{2}$ is equal to?