Question

Which binomial is a factor of 49x2 + 84 xy + 36y2?

Answer 1

Answer:

(7x+6y) is a binomial factor of the given expression  $49x^2+84xy+36y^2$

Therefore  $49x^2+84xy+36y^2=(7x+6y)(7x+6y)$

Step-by-step explanation:

Given expression is $49x^2+84xy+36y^2$

To find the binomial factor :

$49x^2+84xy+36y^2$

Rewritting the above expression as

$=7^2x^2+2(7)(6)xy+6^2y^2$

$=(7x)^2+2(7x)(6y)+(6y)^2$

$=(7x+6y)^2$ ( using the formula $=(a+b)^2=a^2+2ab+b^2$ here a=7x and y=6y )

$=(7x+6y)(7x+6y)$ ( using the formula $=(a+b)^2=(a+b)(a+b)$ )

Therefore  $49x^2+84xy+36y^2=(7x+6y)(7x+6y)$

(7x+6y) is a binomial factor of the given expression  $49x^2+84xy+36y^2$