Q. 5.50 - Intermediate Algebra

Question

Multiply : (a)  (-6b⁴)(-9b⁵)

                 (b) $\left(\frac{2}{3}{r}^{5}s\right)\left(12r^6{s}^7\right)$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(a\right) By multiply the binomials u\sin g distributive property , we get \\ (-6b^4)(-9b^5) \\ 54b^9 \\ \left(b\right) By multiply the binomials u\sin g distributive property , we get \\ \left(\frac{2}{3}{r}^{5}s\right)\left(12r^6{s}^7\right) \\ 8r^{11}{s}^8 \end{gathered}$$

Step 1

Given Information;

$$\begin{gathered} \left(a\right) (-6b^4)(-9b^5) \\ \left(b\right) \left(\frac{2}{3}{r}^{5}s\right)\left(12r^6{s}^7\right) \end{gathered}$$

Step 2.

Commutative Property of Multiplication

• The Commutative property states that " changing the order of the operands does not change the result."
• The commutative property for addition is A + B = B + A
• The commutative property for multiplication is A × B = B × A

Part(a) Step1. Multiply by commutative property.

$$\begin{gathered} \left(a\right) (-6b^4)(-9b^5) \\ use commutative property (-6)\times (-9)\times b^4\times b^5 \\ Multiple 54b^{4+5} \\ 54b^9 \end{gathered}$$

Part(b) Step1. Multiply by commutative property.

$$\begin{gathered} \left(b\right) \left(\frac{2}{3}{r}^{5}s\right)\left(12r^6{s}^7\right) \\ Use commutative property \frac{2}{3}\times 12\times r^5\times s\times r^6\times s^7 \\ Multiple 8\times r^{5+6}\times s^{1+7} \\ 8r^{11}{s}^8 \end{gathered}$$