Solve (3a+8b)(-4a+7b)|7

$$( 3 a + 8 b ) ( - 4 a + 7 b ) | 7$$

Evaluate

$$7\left(7b-4a\right)\left(3a+8b\right)$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$\left(3a+8b\right)\left(-4a+7b\right)\times 7$$

Apply the distributive property by multiplying each term of 3a+8b by each term of -4a+7b.

$$\left(-12a^{2}+21ab-32ba+56b^{2}\right)\times 7$$

Combine 21ab and -32ba to get -11ab.

$$\left(-12a^{2}-11ab+56b^{2}\right)\times 7$$

Use the distributive property to multiply -12a^{2}-11ab+56b^{2} by 7.

$$-84a^{2}-77ab+392b^{2}$$

Differentiate w.r.t. a

$$-168a-77b$$