Question

81(x+1)^2+90(x+1)(y+2)+25(y+2)^2 factorise

Answer 1

Answer:

Factories form of the expression is $81(x+1)^2+90(x+1)(y+2)+25(y+2)^2=(9x+5y+19)(9x+5y+19)$        

Step-by-step explanation:

Given : Expression $81(x+1)^2+90(x+1)(y+2)+25(y+2)^2$

To find : Factories the expression?

Solution :

The given expression $81(x+1)^2+90(x+1)(y+2)+25(y+2)^2$ is in the form of $a^2+2ab+b^2$ in which

$a=9(x+1)$

$b=5(y+2)$

We know,  $a^2+2ab+b^2=(a+b)^2$

Substitute a and b,

$(9(x+1))^2+2(9(x+1))(5(y+2))+(5(y+2))^2=((9(x+1))+(5(y+2)))^2$

$81(x+1)^2+90(x+1)(y+2)+25(y+2)^2=(9x+9+5y+10)^2$

$81(x+1)^2+90(x+1)(y+2)+25(y+2)^2=(9x+5y+19)^2$

$81(x+1)^2+90(x+1)(y+2)+25(y+2)^2=(9x+5y+19)(9x+5y+19)$

Therefore, factories form of the expression is $81(x+1)^2+90(x+1)(y+2)+25(y+2)^2=(9x+5y+19)(9x+5y+19)$

Answer 2

Given:

$81(x+1)^2+90(x+1)(y+2)+25(y+2)^2$

To factorize the given expression

Solution:

$81(x+1)^2+90(x+1)(y+2)+25(y+2)^2$

$(9(x+1))^2+2\times 9(x+1)\times 5(y+2)+(5(y+2))^2$

We know that

$a^2+2ab+b^2=(a+b)^2$

Using the formula

$(9(x+1)+5(y+2))^2$

$(9(x+1)+5(y+2))(9(x+1)+5(y+2))$

$(9x+9+5y+10)(9x+9+5y+10)$

$(9x+5y+19)(9x+5y+19)$