Question

Find each product.

$\left(x-\mathbf{3}\right)\left(x^2+\mathbf{5}x-\mathbf{6}\right)$

Short answer

The product of$\left(x-3\right)\left(x^2+5x-6\right)$ is $x^3+\mathbf{2}{x}^2-\mathbf{21}x+\mathbf{18}$.

Step-by-step solution

Step 1. Write distributive property.

For any numbers,$a,b$ and c, width="124">ab+c=ab+ac.

Step 2. Apply distributive property.

Apply distributive property to the given expression.

$x\left(x^2+5x-6\right)+\left(-3\right)\left(x^2+5x-6\right)=x\cdot x^2+x\cdot 5x-x\cdot 6-3\cdot x^2-3\cdot 5x+3\cdot 6$

Step 3. Multiply and simplify.

Multiply terms in the above expression and simplify it further.

$x^3+5x^2-6x-3x^2-15x+18=x^3+2x^2-21x+18$

Therefore, the product of$\left(x-3\right)\left(x^2+5x-6\right)$ is $x^3+2x^2-21x+18$.