Question

Factorise : (x² + 8x)(x² + 8x + 5) - 14

Answer 1

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

❄❄❄ FACTORISATION ❄❄❄

➡ We factorise a given algebric expression to obtain its product of factors.

➡ EXAMPLE 1 : 2x-4 = 2(x-2) [ANSWER]

➡ EXAMPLE 2 : (2a+3)² = (2a)²+2×2a×3+(3)²

= 4a²+12a+9 [ANSWER]

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❄❄❄ SOLUTION ❄❄❄

(x²+8x) (x²+8x+5) -14

Let (x²+8x) = 'a'.

So, a (a+5) - 14
= a²+5a-14
= a²+(7-2)a-14
= a²+7a-2a-14
= a(a+7)-2(a+7)
= (a+7)(a-2)

Now, putting the value of 'a' in its actual place, we get :-

(x²+8x+7) (x²+8x-2)
= {(x²+(7+1)x+7)} (x²+8x-2)
= (x²+7x+x+7) (x²+8x-2)
= {x(x+7)+1(x+7)} (x²+8x-2)
= (x+1) (x+7) (x²+8x-2) [ANSWER]

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⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

Answer 2

Yo!
Your Answer.

Factorise : (x² + 8x)(x² + 8x + 5) - 14

$\mathfrak{\underline{Solution\: : }}$

Let x² + 8x = a

So,
a(a+5)-14

a² + 5a - 14

$\bold{\underline{middle\:term\: splitting}}$

a² + (7-2)a - 14

a² + 7a - 2a -14

a(a+7)-2(a+7)

(a-2) (a+7)

$\mathsf{Now , put \: a = x^2 + 8x }$

(x² + 8x +7)(x² + 8x -2)

$\bold{\underline{middle\:term\: splitting}}$

{x² + (7+1)x + 7} (x² + 8x -2)

{x²+ 7x+x+7} (x² + 8x -2)

{x(x+7)+1(x+7)} (x² + 8x - 2)

$\bold{(x+7) \:(x+1)\: (x^2 + 8x - 2)}$ [Ans.]

HOPE IT HELPS!