Solve left(5x+2yright)^2-left(2x+5yright)^2

$${ \left(5x+2y \right) }^{ 2 } - { \left(2x+5y \right) }^{ 2 }$$

Evaluate

$$21\left(x^{2}-y^{2}\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2y\right)^{2}.

$$25x^{2}+20xy+4y^{2}-\left(2x+5y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5y\right)^{2}.

$$25x^{2}+20xy+4y^{2}-\left(4x^{2}+20xy+25y^{2}\right)$$

To find the opposite of 4x^{2}+20xy+25y^{2}, find the opposite of each term.

$$25x^{2}+20xy+4y^{2}-4x^{2}-20xy-25y^{2}$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}+20xy+4y^{2}-20xy-25y^{2}$$

Combine 20xy and -20xy to get 0.

$$21x^{2}+4y^{2}-25y^{2}$$

Combine 4y^{2} and -25y^{2} to get -21y^{2}.

$$21x^{2}-21y^{2}$$

Expand

$$21x^{2}-21y^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2y\right)^{2}.

$$25x^{2}+20xy+4y^{2}-\left(2x+5y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5y\right)^{2}.

$$25x^{2}+20xy+4y^{2}-\left(4x^{2}+20xy+25y^{2}\right)$$

To find the opposite of 4x^{2}+20xy+25y^{2}, find the opposite of each term.

$$25x^{2}+20xy+4y^{2}-4x^{2}-20xy-25y^{2}$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}+20xy+4y^{2}-20xy-25y^{2}$$

Combine 20xy and -20xy to get 0.

$$21x^{2}+4y^{2}-25y^{2}$$

Combine 4y^{2} and -25y^{2} to get -21y^{2}.

$$21x^{2}-21y^{2}$$