CPM Homework Help : AC Problem 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).

$\left(4x-1\right)\left(3x+5\right)$
Answer (a):
Generic rectangle left edge top $4x$
interior top left $12x^2$
interior top right $20x$
left edge bottom $-1$
interior bottom left $-3x$
interior bottom right $-5$
bottom edge left $3x$
bottom edge right $5$
$12x^2+17x-5$
$12x^2\left(-5\right)=-3x\left(20x\right)$
$-60x^2=-60x^2$

$\left(2x-7\right)^2$
Hint (b):
$\left(2x-7\right)^2=\left(2x-7\right)\left(2x-7\right)$