Question

$\bold \pink{factorise \: the \: following : - }$
$\bold{i) \: x \: ( {x}^{2} - 1 )(x + 2) - 8}$
$\bold{ii)(a - 1) {x}^{2} + {a}^{2}xy + ( a+ 1) {y}^{2} }$
☺☺☺☺☺☺☺☺☺

Give correct answer step by step ✅✅✅✅

❌❌Don't Spam ❌❌

☑☑☑☑☑Correct answer will be marked as Brainlist ☑☑☑☑☑​

Answer 1

$\huge\underline\bold{\purple{\fbox{♡ANSWER♡}}}$

x(x² - 1)(x + 2) - 8

= x(x - 1)[(x + 1)(x + 2)] - 8

= (x² - x)(x² + 3x + 2) - 8

= (x² + x - 2x)(x² + x + 2x + 2) - 8

let t = x² + x

= (t - 2x)(t + 2x + 2) - 8

= (t² + (2x + 2 - 2)t - 4x² - 4x - 8

= t² + 2t - 4(x² + x) - 8

= t² + 2t - 4t - 8

= t² - 2t - 8

= t² - 4t + 2t - 8

= t(t - 4) + 2(t - 4)

= (t + 2)(t - 4)

now putting t = (x² + x)

= (x² + x + 2)(x² + x - 4)

$\huge\underline\bold{\red{\fbox{ans:-2}}}$

(a - 1)x² + a²xy + (a + 1)y²

= (a - 1)x² + (a² - 1 + 1)xy + (a + 1)y²

= (a - 1)x² + {(a - 1)(a + 1) + 1}xy + (a + 1)y²

= (a - 1)x² + (a - 1)(a + 1)xy + xy + (a + 1)y²

= (a - 1)x{x + (a + 1)y} + y{x + (a + 1)y}

= (x + ay + y)(ax - x + y)

$<marquee behavior-move><font color="maroon"><h1>★ThanK YoU✌✌</ ht></marquee>$

Answer 2

Answer:

x(x² - 1)(x + 2) - 8

= x(x - 1)[(x + 1)(x + 2)] - 8

= (x² - x)(x² + 3x + 2) - 8

= (x² + x - 2x)(x² + x + 2x + 2) - 8

let t = x² + x

= (t - 2x)(t + 2x + 2) - 8

= (t² + (2x + 2 - 2)t - 4x² - 4x - 8

= t² + 2t - 4(x² + x) - 8

= t² + 2t - 4t - 8

= t² - 2t - 8

= t² - 4t + 2t - 8

= t(t - 4) + 2(t - 4)

= (t + 2)(t - 4)

now putting t = (x² + x)

= (x² + x + 2)(x² + x - 4)