Solve left(3x+2yright)^2-4left(x-yright)^2

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

Evaluate

$$5x\left(x+4y\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.

$$9x^{2}+12xy+4y^{2}-4\left(x-y\right)^{2}$$

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

$$9x^{2}+12xy+4y^{2}-4\left(x^{2}-2xy+y^{2}\right)$$

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

$$9x^{2}+12xy+4y^{2}-4x^{2}+8xy-4y^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+12xy+4y^{2}+8xy-4y^{2}$$

Combine 12xy and 8xy to get 20xy.

$$5x^{2}+20xy+4y^{2}-4y^{2}$$

Combine 4y^{2} and -4y^{2} to get 0.

$$5x^{2}+20xy$$

Expand

$$5x^{2}+20xy$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.

$$9x^{2}+12xy+4y^{2}-4\left(x-y\right)^{2}$$

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

$$9x^{2}+12xy+4y^{2}-4\left(x^{2}-2xy+y^{2}\right)$$

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

$$9x^{2}+12xy+4y^{2}-4x^{2}+8xy-4y^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+12xy+4y^{2}+8xy-4y^{2}$$

Combine 12xy and 8xy to get 20xy.

$$5x^{2}+20xy+4y^{2}-4y^{2}$$

Combine 4y^{2} and -4y^{2} to get 0.

$$5x^{2}+20xy$$