Question

(viii) (x2 - 4x + 4) - 81
2. Factorise:​

Answer 1

Question :

$\text{Factorise}\:\:\:(x^{2} - 4x+4)-81$

Solution :

$\implies x^{2} -4x+4-81=0$

$\implies x^{2} -4x-77=0$

$\implies x^{2} -11x+7x-77=0$

$\implies x(x-11)+7(x-11)=0$

$\implies(x+7)(x-11)=0$

$\implies x= -7 (or) 11$

Verification :

$\text{Substitute the values of x in equation}$

(i) Substitute x = 11

$\implies x^{2} - 4x+4-81 = 0 \\\implies x^{2} -4x-77 = 0 \\\implies {(11)}^{2} -4(11)-77 = 0\\\implies 121 - 44 - 77 = 0\\\implies 121 - 121 = 0 \\ \implies 0 = 0$

(ii) substitute x = -7

$\implies x^{2} -4x+4-81=0 \\\implies x^{2} - 4x -77 = 0 \\\implies {(-7)}^{2} - 4(-7) -77 =0 \\ \implies 49 + 28 - 77 =0 \\ \implies 77 - 77 = 0 \\ \implies 0 = 0$

Hence Verified

Answer 2

Question :

$\text{Factorise}\:\:\:(x^{2} - 4x+4)-81$

Solution :

$\implies x^{2} -4x+4-81=0$

$\implies x^{2} -4x-77=0$

$\implies x^{2} -11x+7x-77=0$

$\implies x(x-11)+7(x-11)=0$

$\implies(x+7)(x-11)=0$

$\implies x= -7 (or) 11$

Verification :

$\text{Substitute the values of x in equation}$

(i) Substitute x = 11

$\implies x^{2} - 4x+4-81 = 0 \\\implies x^{2} -4x-77 = 0 \\\implies {(11)}^{2} -4(11)-77 = 0\\\implies 121 - 44 - 77 = 0\\\implies 121 - 121 = 0 \\ \implies 0 = 0$

(ii) substitute x = -7

$\implies x^{2} -4x+4-81=0 \\\implies x^{2} - 4x -77 = 0 \\\implies {(-7)}^{2} - 4(-7) -77 =0 \\ \implies 49 + 28 - 77 =0 \\ \implies 77 - 77 = 0 \\ \implies 0 = 0$

Hence Verified