Solve (-q+1)(12q^2-5q+7)

$$( - q + 1 ) ( 12 q ^ { 2 } - 5 q + 7 )$$

Evaluate

$$\left(1-q\right)\left(12q^{2}-5q+7\right)$$

Solution Steps

Use the distributive property to multiply -q+1 by 12q^{2}-5q+7.

$$12\left(-q\right)q^{2}-5\left(-q\right)q+7\left(-q\right)+12q^{2}-5q+7$$

Multiply -5 and -1 to get 5.

$$12\left(-q\right)q^{2}+5qq+7\left(-q\right)+12q^{2}-5q+7$$

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

$$12\left(-q\right)q^{2}+5q^{2}+7\left(-q\right)+12q^{2}-5q+7$$

Combine 5q^{2} and 12q^{2} to get 17q^{2}.

$$12\left(-q\right)q^{2}+17q^{2}+7\left(-q\right)-5q+7$$

Multiply 12 and -1 to get -12.

$$-12qq^{2}+17q^{2}+7\left(-1\right)q-5q+7$$

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

$$-12q^{3}+17q^{2}+7\left(-1\right)q-5q+7$$

Multiply 7 and -1 to get -7.

$$-12q^{3}+17q^{2}-7q-5q+7$$

Combine -7q and -5q to get -12q.

$$-12q^{3}+17q^{2}-12q+7$$

Expand

$$7-12q+17q^{2}-12q^{3}$$

Solution Steps

Use the distributive property to multiply -q+1 by 12q^{2}-5q+7.

$$12\left(-q\right)q^{2}-5\left(-q\right)q+7\left(-q\right)+12q^{2}-5q+7$$

Multiply -5 and -1 to get 5.

$$12\left(-q\right)q^{2}+5qq+7\left(-q\right)+12q^{2}-5q+7$$

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

$$12\left(-q\right)q^{2}+5q^{2}+7\left(-q\right)+12q^{2}-5q+7$$

Combine 5q^{2} and 12q^{2} to get 17q^{2}.

$$12\left(-q\right)q^{2}+17q^{2}+7\left(-q\right)-5q+7$$

Multiply 12 and -1 to get -12.

$$-12qq^{2}+17q^{2}+7\left(-1\right)q-5q+7$$

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

$$-12q^{3}+17q^{2}+7\left(-1\right)q-5q+7$$

Multiply 7 and -1 to get -7.

$$-12q^{3}+17q^{2}-7q-5q+7$$

Combine -7q and -5q to get -12q.

$$-12q^{3}+17q^{2}-12q+7$$