Solve {l}{16(x-2)^2}{-25(y+1)^2}

$$\left. \begin{array} { l } { 16 ( x - 2 ) ^ { 2 } } \\ { - 25 ( y + 1 ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$\left(4x-5y-13\right)\left(4x+5y-3\right)$$

Solution Steps

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

$$16\left(x^{2}-4x+4\right)-25\left(y+1\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-4x+4.

$$16x^{2}-64x+64-25\left(y+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+1\right)^{2}.

$$16x^{2}-64x+64-25\left(y^{2}+2y+1\right)$$

Use the distributive property to multiply -25 by y^{2}+2y+1.

$$16x^{2}-64x+64-25y^{2}-50y-25$$

Subtract 25 from 64 to get 39.

$$16x^{2}-64x+39-25y^{2}-50y$$

Expand

$$16x^{2}-64x-25y^{2}-50y+39$$

Solution Steps

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

$$16\left(x^{2}-4x+4\right)-25\left(y+1\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-4x+4.

$$16x^{2}-64x+64-25\left(y+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+1\right)^{2}.

$$16x^{2}-64x+64-25\left(y^{2}+2y+1\right)$$

Use the distributive property to multiply -25 by y^{2}+2y+1.

$$16x^{2}-64x+64-25y^{2}-50y-25$$

Subtract 25 from 64 to get 39.

$$16x^{2}-64x+39-25y^{2}-50y$$