Solve 3left(x+yright)^2-2yleft(y+yright)^2

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

Evaluate

$$-8y^{3}+3\left(x+y\right)^{2}$$

Solution Steps

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

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

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

$$3x^{2}+6xy+3y^{2}-2y\left(y+y\right)^{2}$$

Combine y and y to get 2y.

$$3x^{2}+6xy+3y^{2}-2y\times \left(2y\right)^{2}$$

Expand \left(2y\right)^{2}.

$$3x^{2}+6xy+3y^{2}-2y\times 2^{2}y^{2}$$

Calculate 2 to the power of 2 and get 4.

$$3x^{2}+6xy+3y^{2}-2y\times 4y^{2}$$

Multiply 2 and 4 to get 8.

$$3x^{2}+6xy+3y^{2}-8yy^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3x^{2}+6xy+3y^{2}-8y^{3}$$

Expand

$$3x^{2}+6xy-8y^{3}+3y^{2}$$

Solution Steps

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

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

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

$$3x^{2}+6xy+3y^{2}-2y\left(y+y\right)^{2}$$

Combine y and y to get 2y.

$$3x^{2}+6xy+3y^{2}-2y\times \left(2y\right)^{2}$$

Expand \left(2y\right)^{2}.

$$3x^{2}+6xy+3y^{2}-2y\times 2^{2}y^{2}$$

Calculate 2 to the power of 2 and get 4.

$$3x^{2}+6xy+3y^{2}-2y\times 4y^{2}$$

Multiply 2 and 4 to get 8.

$$3x^{2}+6xy+3y^{2}-8yy^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3x^{2}+6xy+3y^{2}-8y^{3}$$