Answer:
(7x+6y) is a binomial factor of the given expression [tex]49x^2+84xy+36y^2[/tex]
Therefore [tex]49x^2+84xy+36y^2=(7x+6y)(7x+6y)[/tex]
Step-by-step explanation:
Given expression is [tex]49x^2+84xy+36y^2[/tex]
To find the binomial factor :
[tex]49x^2+84xy+36y^2[/tex]
Rewritting the above expression as
[tex]=7^2x^2+2(7)(6)xy+6^2y^2[/tex]
[tex]=(7x)^2+2(7x)(6y)+(6y)^2[/tex]
[tex]=(7x+6y)^2[/tex] ( using the formula [tex]=(a+b)^2=a^2+2ab+b^2[/tex] here a=7x and y=6y )
[tex]=(7x+6y)(7x+6y)[/tex] ( using the formula [tex]=(a+b)^2=(a+b)(a+b)[/tex] )
Therefore [tex]49x^2+84xy+36y^2=(7x+6y)(7x+6y)[/tex]
(7x+6y) is a binomial factor of the given expression [tex]49x^2+84xy+36y^2[/tex]
