Q 5.53 - Intermediate Algebra

Question

Multiple : (a)$(x+8)(x+9)$ 

                (b) $(3c+4)(5c-2)$

Step-by-Step Solution

Answer

(a) $$\begin{gathered} x^2+9\times x+8\times x+8\times 9 \\ {x}^2+9x+8x+72 \\ {x}^2+17x+72 \end{gathered}$$$$\begin{gathered} x\times x+x\times 9+8\times x+8\times 9 \\ {x}^2+9x+8x+72 \\ {x}^2+17x+72 \end{gathered}$$

(b) $$\begin{gathered} 3c\times 5c-3c\times 2+4\times 5c-8 \\ 15c^2-6c+20c-8 \\ 15c^2+14c-8 \end{gathered}$$

Step 1

Given Information:

$$\begin{gathered} \left(a\right) (x+8)(x+9) \\ \left(b\right) (3c+4)(5c-2) \end{gathered}$$

Step 2

Distributive Property:

Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis.

Step 3

$\left(a\right) (x+8)(x+9)$

Distribute $(x+9)$: $x(x+9)+8(x+9)$

Distribute again:  $x^2+9x+8x+72$

Combine like terms: $x^2+17x+72$

Step 4

(b)$(3c+4)(5c-2)$

Distribute:                 $3c(5c-2)+4(5c-2)$

Distribute again:      $15c^2-6c+20c-8$

Combine like terms: $15c^2+14c-8$