Simplify in factors:
$3 {(x - 1)}^{2} + 5 (x - 1) (x + 4) - 2 {(x + 4)}^{2}$

(2 x + 7) (3 x - 7)

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(x - 7) (2 x + 7)

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(2 x - 3) (x + 7)

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(2 x - 7) (3 x + 7)

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Solution

The correct option is D $(2 x - 7) (3 x + 7)$
We solve the given expression $3 (x - 1)^{2} + 5 (x - 1) (x + 4) - 2 (x + 4)^{2}$ as follows:

$3 (x - 1)^{2} + 5 (x - 1) (x + 4) - 2 (x + 4)^{2} = 3 [x^{2} + 1^{2} - (2 \times x \times 1)] + 5 [(x \times x) + (x \times 4) - (1 \times x) - (1 \times 4)] - 2 [x^{2} + 4^{2} + (2 \times x \times 4)]$

$(∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b, (a + b)^{2} = a^{2} + b^{2} + 2 a b) = 3 (x^{2} + 1 - 2 x) + 5 (x^{2} + 3 x - 4) - 2 (x^{2} + 16 + 8 x) = 3 x^{2} + 3 - 6 x) + 5 x^{2} + 15 x - 20 - 2 x^{2} + 32 + 16 x = 6 x^{2} - 7 x - 49$

Now, we factorize the equation $6 x^{2} - 7 x - 49$ as shown below:
$6 x^{2} - 7 x - 49 = 6 x^{2} - 21 x + 14 x - 49 = 3 x (2 x - 7) + 7 (2 x - 7) = (2 x - 7) (3 x + 7)$

Hence, the factors are $(2 x - 7) (3 x + 7)$ .

Suggest Corrections

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