Solve -3(x-8)(x+7)^3

$$- 3 ( x - 8 ) ( x + 7 ) ^ { 3 }$$

Expand

$$8232+2499x+63x^{2}-39x^{3}-3x^{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+7\right)^{3}.

$$-3\left(x-8\right)\left(x^{3}+21x^{2}+147x+343\right)$$

Use the distributive property to multiply -3 by x-8.

$$\left(-3x+24\right)\left(x^{3}+21x^{2}+147x+343\right)$$

Use the distributive property to multiply -3x+24 by x^{3}+21x^{2}+147x+343 and combine like terms.

$$-3x^{4}-39x^{3}+63x^{2}+2499x+8232$$

Evaluate

$$-3\left(x-8\right)\left(x+7\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+7\right)^{3}.

$$-3\left(x-8\right)\left(x^{3}+21x^{2}+147x+343\right)$$

Use the distributive property to multiply -3 by x-8.

$$\left(-3x+24\right)\left(x^{3}+21x^{2}+147x+343\right)$$

Use the distributive property to multiply -3x+24 by x^{3}+21x^{2}+147x+343 and combine like terms.

$$-3x^{4}-39x^{3}+63x^{2}+2499x+8232$$