Solve 3y^2-6y^2+3x^2

$$3 y ^ { 2 } - 6 y ^ { 2 } + 3 x ^ { 2 }$$

Factor

$$3\left(x-y\right)\left(x+y\right)$$

Solution Steps

Factor out 3.

$$3\left(y^{2}-2y^{2}+x^{2}\right)$$

Consider y^{2}-2y^{2}+x^{2}. Multiply and combine like terms.

$$x^{2}-y^{2}$$

Consider x^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-y\right)\left(x+y\right)$$

Rewrite the complete factored expression.

$$3\left(x-y\right)\left(x+y\right)$$

Evaluate

$$3\left(x^{2}-y^{2}\right)$$

Solution Steps

Combine 3y^{2} and -6y^{2} to get -3y^{2}.

$$-3y^{2}+3x^{2}$$