So we must factor the following expression:
[tex]3x^2+6xy+3y^2[/tex]First of all is important to notice that all terms are multiplied by an integer that is a multiple of 3. Then 3 is a common factor and we can re-write the expression like this:
[tex]3x^2+6xy+3y^2=3\cdot(x^2+2xy+y^2)[/tex]Now let's have a look at the expression inside parenthesis but first let's recall the expression for the square of a binomial. For two real numbers a and b we get:
[tex](a+b)^2=a^2+2ab+b^2[/tex]If you replace a and b with x and y we get the following:
[tex]a^2+2ab+b^2\rightarrow x^2+2xy+y^2[/tex]Which means that:
[tex]x^2+2xy+y^2=(x+y)^2[/tex]Then the factored form of the original expression and answer to this problem is:
[tex]3(x+y)^2[/tex]