Question

Factoaise the following using the identity
a² b²=(a-b) (a+b)
36 (P+q)^2-64(P-q)^2​

Answer 1

Step-by-step explanation:

$36 {(p + q)}^{2} - 64 {(p - q)}^{2}$

$= {6}^{2} {(p + q)}^{2} - {8}^{2} {(p - q)}^{2}$

$= {(6(p + q))}^{2} - {(8(p - q))}^{2}$

$= {(6p + 6q)}^{2} - {(8p - 8q)}^{2}$

$= (6p + 6q + 8p - 8q)(6p + 6q - 8p + 8q)$

$= (14p - 2q)(14q - 2p)$

Hence, factorised.

I hope it helps you. If you have any doubts, then don't hesitate to ask.

Answer 2

$\huge{\red{-Answer-}}$

a(a+b)=36 ...(i)

b(a+b)=64 ...(ii)

On dividing (i) by (ii), we get b/a= 16/9

⇒b= 9/16a ...(iii)

∴(i)becomes

a 2+ab−36=0⇒a 2 +a( 9/16a)−36=0

⇒ 9/25a 2 =36

⇒a 2= 25/324

⇒a= 5/18 (∵ a is positive.

b= 9/16× 5/18

⇒b= 5/32

a−b= 5/18− 5/32=− 5/14=−2.8