Q5.63 - Intermediate Algebra

Question

Multiply :$\left(a\right) {(x+9)}^2\left(b\right) {(2c-d)}^2$

Step-by-Step Solution

Answer

$$\begin{gathered} Open the identity and Multiply \\ \left(a\right) {(x+9)}^2 \\ x^2+81+18x \\ \left(b\right) {(2c-d)}^2 \\ 4c^2+d^2-4cd \end{gathered}$$

Step 1

$$\begin{gathered} Given Information: \\ \left(a\right) {(x+9)}^2\left(b\right) {(2c-d)}^2 \end{gathered}$$

Step 2

he square of this expression is written as ${(a-b)}^2$ in mathematical form and it is expanded as $a^2-2ab+b^2$ mathematically.

In mathematics, this algebraic identity is used as a formula and it is called in the following three ways.

1. The square of difference of the terms formula.
2. The square of a binomial identity.
3. The special binomial product rule.

Part(a) Step1 Use ( a + b ) 2 = a 2 + b 2 - 2 a b

$$\begin{gathered} \left(a\right) \\ 1. Square the first term x^2 \\ 2. Square the last term x^2+81 \\ 3. Double their product x^2+81+2\times x\times 9 \\ Simplify x^2+18x+81 \end{gathered}$$

Part(b) Step1. Use ( a - b ) 2 = a 2 + b 2 - 2 a b

$$\begin{gathered} \left(b\right) \\ 1. Square the first term 4c^2 \\ 2. Square the last term 4c^2+d^2 \\ 3. Double their product 4c^2+d^2+2\times 2c\times (-d) \\ Simplify 4c^2-4cd+d^2 \end{gathered}$$