Solve (3x-4)^2*-x+19

$$( 3 x - 4 ) ^ { 2 } * - x + 19$$

Evaluate

$$-x\left(3x-4\right)^{2}+19$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$\left(9x^{2}-24x+16\right)\left(-x\right)+19$$

Use the distributive property to multiply 9x^{2}-24x+16 by -x.

$$9x^{2}\left(-x\right)-24x\left(-x\right)+16\left(-x\right)+19$$

Multiply -24 and -1 to get 24.

$$9x^{2}\left(-x\right)+24xx+16\left(-x\right)+19$$

Multiply x and x to get x^{2}.

$$9x^{2}\left(-x\right)+24x^{2}+16\left(-x\right)+19$$

Multiply 9 and -1 to get -9.

$$-9x^{2}x+24x^{2}+16\left(-1\right)x+19$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-9x^{3}+24x^{2}+16\left(-1\right)x+19$$

Multiply 16 and -1 to get -16.

$$-9x^{3}+24x^{2}-16x+19$$

Expand

$$19-16x+24x^{2}-9x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$\left(9x^{2}-24x+16\right)\left(-x\right)+19$$

Use the distributive property to multiply 9x^{2}-24x+16 by -x.

$$9x^{2}\left(-x\right)-24x\left(-x\right)+16\left(-x\right)+19$$

Multiply -24 and -1 to get 24.

$$9x^{2}\left(-x\right)+24xx+16\left(-x\right)+19$$

Multiply x and x to get x^{2}.

$$9x^{2}\left(-x\right)+24x^{2}+16\left(-x\right)+19$$

Multiply 9 and -1 to get -9.

$$-9x^{2}x+24x^{2}+16\left(-1\right)x+19$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-9x^{3}+24x^{2}+16\left(-1\right)x+19$$

Multiply 16 and -1 to get -16.

$$-9x^{3}+24x^{2}-16x+19$$