Answer:
Factors of the term [tex]4x^2 + 12xy + 9y^2[/tex] are [tex]\mathbf{(2x+3y)(2x+3y)\:or\:(2x+3y)^2}[/tex]
Step-by-step explanation:
We need to factor the term [tex]4x^2 + 12xy + 9y^2[/tex]
We can factor the term by breaking the middle term.
Middle term 12xy should be broken is such a way that:
- Their sum result in middle term, 12xy
- Their product result in product of first and last term i.e 4x^2(9y^2) = 36x^2y^2
Now, if we break 12xy into 6xy and 6xy
- sum of 6xy and 6xy is 12xy
- product of 6xy and 6xy is 36x^2y^2
So, our both conditions are fulfilled.
Breaking the middle terms and finding factors
[tex]4x^2+12xy+9y^2\\=4x^2+6xy+6xy+9y^2\\=2x(2x+3y)+3y(2x+3y)\\=(2x+3y)(2x+3y)\\=(2x+3y)^2[/tex]
So, factors of the term [tex]4x^2 + 12xy + 9y^2[/tex] are [tex]\mathbf{(2x+3y)(2x+3y)\:or\:(2x+3y)^2}[/tex]
