Solve 25left(x+yright)^2-left(x-yright)^2

$$25 { \left(x+y \right) }^{ 2 } - { \left(x-y \right) }^{ 2 }$$

Evaluate

$$4\left(2x+3y\right)\left(3x+2y\right)$$

Solution Steps

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

$$25\left(x^{2}+2xy+y^{2}\right)-\left(x-y\right)^{2}$$

Use the distributive property to multiply 25 by x^{2}+2xy+y^{2}.

$$25x^{2}+50xy+25y^{2}-\left(x-y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-\left(x^{2}-2xy+y^{2}\right)$$

To find the opposite of x^{2}-2xy+y^{2}, find the opposite of each term.

$$25x^{2}+50xy+25y^{2}-x^{2}+2xy-y^{2}$$

Combine 25x^{2} and -x^{2} to get 24x^{2}.

$$24x^{2}+50xy+25y^{2}+2xy-y^{2}$$

Combine 50xy and 2xy to get 52xy.

$$24x^{2}+52xy+25y^{2}-y^{2}$$

Combine 25y^{2} and -y^{2} to get 24y^{2}.

$$24x^{2}+52xy+24y^{2}$$

Expand

$$24x^{2}+52xy+24y^{2}$$

Solution Steps

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

$$25\left(x^{2}+2xy+y^{2}\right)-\left(x-y\right)^{2}$$

Use the distributive property to multiply 25 by x^{2}+2xy+y^{2}.

$$25x^{2}+50xy+25y^{2}-\left(x-y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-\left(x^{2}-2xy+y^{2}\right)$$

To find the opposite of x^{2}-2xy+y^{2}, find the opposite of each term.

$$25x^{2}+50xy+25y^{2}-x^{2}+2xy-y^{2}$$

Combine 25x^{2} and -x^{2} to get 24x^{2}.

$$24x^{2}+50xy+25y^{2}+2xy-y^{2}$$

Combine 50xy and 2xy to get 52xy.

$$24x^{2}+52xy+25y^{2}-y^{2}$$

Combine 25y^{2} and -y^{2} to get 24y^{2}.

$$24x^{2}+52xy+24y^{2}$$