### Home > CAAC > Chapter 8 > Lesson 8.1.1 > Problem8-7

8-7.

Multiply the expressions below using a generic rectangle. Then verify Casey's pattern (that the product of one diagonal equals the product of the other diagonal).

1. $(4x−1)(3x+5)$

 $4x$ $12x^2$ $20x$ $-1$ $-3x$ $-5$ $3x$ $5$

$12x^2 + 17x − 5$

$12x^2(−5) = −3x(20x)$
$−60x^2 = −60x^2$

1. $(2x−7)^2$

(2x − 7)² = (2x − 7)(2x − 7)