Solve 4(x-y)^2-25(x+y)^2=

$$4 ( x - y ) ^ { 2 } - 25 ( x + y ) ^ { 2 } =$$

Evaluate

$$-\left(3x+7y\right)\left(7x+3y\right)$$

Solution Steps

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

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

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

$$4x^{2}-8xy+4y^{2}-25\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-25\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-25x^{2}-50xy-25y^{2}$$

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

$$-21x^{2}-8xy+4y^{2}-50xy-25y^{2}$$

Combine -8xy and -50xy to get -58xy.

$$-21x^{2}-58xy+4y^{2}-25y^{2}$$

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

$$-21x^{2}-58xy-21y^{2}$$

Expand

$$-21x^{2}-58xy-21y^{2}$$

Solution Steps

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

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

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

$$4x^{2}-8xy+4y^{2}-25\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-25\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-25x^{2}-50xy-25y^{2}$$

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

$$-21x^{2}-8xy+4y^{2}-50xy-25y^{2}$$

Combine -8xy and -50xy to get -58xy.

$$-21x^{2}-58xy+4y^{2}-25y^{2}$$

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

$$-21x^{2}-58xy-21y^{2}$$