Q19.

Find each product.

$(x - 3) (x^{2} + 5 x - 6)$

Verified

Answer

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

1Step 1. Write distributive property.

For any numbers, $a, b$ and c, width="124" style="max-width: none; vertical-align: -5px;" $a (b + c) = a b + a c$ .

2Step 2. Apply distributive property.

Apply distributive property to the given expression.

$x (x^{2} + 5 x - 6) + (- 3) (x^{2} + 5 x - 6) = x \cdot x^{2} + x \cdot 5 x - x \cdot 6 - 3 \cdot x^{2} - 3 \cdot 5 x + 3 \cdot 6$

3Step 3. Multiply and simplify.

Multiply terms in the above expression and simplify it further.

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

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