Factor completely: (4x−3)^2−(3x+5)^2 PLEASE HELP ASAP!!!

(x - 8)(7x + 2)

Step-by-step explanation:

Given

(4x - 3)² - (3x + 5)² ← expand both using FOIL

= 16x² - 24x + 9 - (9x² + 30x + 25) ← distribute by - 1

= 16x² - 24x + 9 - 9x² - 30x - 25 ← collect like terms

= 7x² - 54x - 16

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 7 × - 16 = - 112 and sum = - 54

The factors are - 56 and + 2

Use these factors to split the x- term

= 7x² - 56x + 2x - 16 ( factor the first/second and third/fourth terms )

= 7x(x - 8) + 2(x - 8) ← factor out (x - 8) from each term

= (x - 8)(7x + 2) ← in factored form