Solve 3(x+2y)^2-13x(x+2y)+4x^2

$$3 ( x + 2 y ) ^ { 2 } - 13 x ( x + 2 y ) + 4 x ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.

$$3\left(x^{2}+4xy+4y^{2}\right)-13x\left(x+2y\right)+4x^{2}$$

Use the distributive property to multiply 3 by x^{2}+4xy+4y^{2}.

$$3x^{2}+12xy+12y^{2}-13x\left(x+2y\right)+4x^{2}$$

Use the distributive property to multiply -13x by x+2y.

$$3x^{2}+12xy+12y^{2}-13x^{2}-26xy+4x^{2}$$

Combine 3x^{2} and -13x^{2} to get -10x^{2}.

$$-10x^{2}+12xy+12y^{2}-26xy+4x^{2}$$

Combine 12xy and -26xy to get -14xy.

$$-10x^{2}-14xy+12y^{2}+4x^{2}$$

Combine -10x^{2} and 4x^{2} to get -6x^{2}.

$$-6x^{2}-14xy+12y^{2}$$

Expand

$$12y^{2}-14xy-6x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.

$$3\left(x^{2}+4xy+4y^{2}\right)-13x\left(x+2y\right)+4x^{2}$$

Use the distributive property to multiply 3 by x^{2}+4xy+4y^{2}.

$$3x^{2}+12xy+12y^{2}-13x\left(x+2y\right)+4x^{2}$$

Use the distributive property to multiply -13x by x+2y.

$$3x^{2}+12xy+12y^{2}-13x^{2}-26xy+4x^{2}$$

Combine 3x^{2} and -13x^{2} to get -10x^{2}.

$$-10x^{2}+12xy+12y^{2}-26xy+4x^{2}$$

Combine 12xy and -26xy to get -14xy.

$$-10x^{2}-14xy+12y^{2}+4x^{2}$$

Combine -10x^{2} and 4x^{2} to get -6x^{2}.

$$-6x^{2}-14xy+12y^{2}$$