Question

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

Answer 1

(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)`

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`