Question

Which expression is equivalent to (x - 2)(x + 4) ?

(x + 1)2 – 9
(x - 1)² – 9
(x + 1)² – 7
(x - 1)² – 7

Answer 1

(x + 1)² - 9

Explanation:

Expand each of the factors using FOIL

(x - 2)(x + 4)

= x² + 4x - 2x - 8 ← collect like terms

= x² + 2x - 8

Now consider the expansions of

(x + 1)² - 9

= x² + 2x + 1 - 9

= x² + 2x - 8 ← equivalent to (x - 2)(x + 4)

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(x - 1)² - 9

= x² - 2x + 1 - 9

= x² - 2x - 8 ← not equivalent to (x - 2)(x + 4)

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(x + 1)² - 7

= x² + 2x + 1 - 7

= x² + 2x - 6 ← not equivalent to (x - 2)(x + 4)

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(x - 1)² - 7

= x² - 2x + 1 - 7

= x² - 2x - 6 ← not equivalent to (x - 2)(x + 4)

Answer 2

Explanation:

hello :

(x + 1)2 – 9 is equivalent to (x - 2)(x + 4)

because (x + 1)2 – 9 =(x + 1)2 – 3²

= (x+1-3)(x+1+3) =(x-2)(x+4)