Solve (5-4x)(5x-6)-3(4x-5)^2

$$( 5 - 4 x ) ( 5 x - 6 ) - 3 ( 4 x - 5 ) ^ { 2 }$$

Evaluate

$$\left(21-17x\right)\left(4x-5\right)$$

Solution Steps

Use the distributive property to multiply 5-4x by 5x-6 and combine like terms.

$$49x-30-20x^{2}-3\left(4x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-5\right)^{2}.

$$49x-30-20x^{2}-3\left(16x^{2}-40x+25\right)$$

Use the distributive property to multiply -3 by 16x^{2}-40x+25.

$$49x-30-20x^{2}-48x^{2}+120x-75$$

Combine -20x^{2} and -48x^{2} to get -68x^{2}.

$$49x-30-68x^{2}+120x-75$$

Combine 49x and 120x to get 169x.

$$169x-30-68x^{2}-75$$

Subtract 75 from -30 to get -105.

$$169x-105-68x^{2}$$

Expand

$$-68x^{2}+169x-105$$

Solution Steps

Use the distributive property to multiply 5-4x by 5x-6 and combine like terms.

$$49x-30-20x^{2}-3\left(4x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-5\right)^{2}.

$$49x-30-20x^{2}-3\left(16x^{2}-40x+25\right)$$

Use the distributive property to multiply -3 by 16x^{2}-40x+25.

$$49x-30-20x^{2}-48x^{2}+120x-75$$

Combine -20x^{2} and -48x^{2} to get -68x^{2}.

$$49x-30-68x^{2}+120x-75$$

Combine 49x and 120x to get 169x.

$$169x-30-68x^{2}-75$$

Subtract 75 from -30 to get -105.

$$169x-105-68x^{2}$$