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Factorize 9( x - 1 ) ^ { 2 } - 16 ( x + 2 ) ^ { 2 }​

1 Answer

7 votes

Answer:

(7x + 5)(- x - 11)

Explanation:

9(x - 1)² - 16(x + 2)² ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

9(x - 1)² - 16(x + 2)²

= [ 3(x - 1) ]² - [4(x + 2) ]² with a = 3(x - 1) and b = 4(x + 2)

= [ 3(x - 1) + 4(x + 2) ] [ 3(x - 1) - 4(x + 2) ] ← distribute parenthesis

= [ 3x - 3 + 4x + 8 ] [ 3x - 3 - 4x - 8 ]

= (7x + 5)(- x - 11 )

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