Solve [(-84)xdiv(-7)x]x-(-9)x*(-5)+(-3)x

$$[ ( - 84 ) x \div ( - 7 ) x ] x - ( - 9 ) x \cdot ( - 5 ) + ( - 3 ) x$$

Evaluate

$$12x\left(x^{2}-4\right)$$

Solution Steps

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

$$\frac{-84x}{-7}x^{2}-\left(-9x\left(-5\right)\right)-3x$$

Divide -84x by -7 to get 12x.

$$12xx^{2}-\left(-9x\left(-5\right)\right)-3x$$

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

$$12x^{3}-\left(-9x\left(-5\right)\right)-3x$$

Multiply -9 and -5 to get 45.

$$12x^{3}-45x-3x$$

Combine -45x and -3x to get -48x.

$$12x^{3}-48x$$

Factor

$$12x\left(x-2\right)\left(x+2\right)$$

Solution Steps

Factor out 3.

$$3\left(4xxx-15x-x\right)$$

Consider 4x^{3}-15x-x. Factor out x.

$$x\left(4x^{2}-16\right)$$

Consider 4x^{2}-15-1. Multiply and combine like terms.

$$4x^{2}-16$$

Consider 4x^{2}-16. Factor out 4.

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

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$12\left(x+2\right)\left(x-2\right)x$$

Simplify.

$$12x\left(x-2\right)\left(x+2\right)$$