Q5.64 - Intermediate Algebra

Question

Multiply: $\left(a\right) {(y+11)}^2\left(b\right) {(4x-5y)}^2$

Step-by-Step Solution

Answer

$$\begin{gathered} Open the identity and multiply \\ \left(a\right) {(y+11)}^2 \\ y^2+121+22y \\ \left(b\right) {(4x-5y)}^2 \\ 16x^2+25y^2-40xy \end{gathered}$$

Step 1

$$\begin{gathered} Given Information \\ \left(a\right) {(y+11)}^2\left(b\right) {(4x-5y)}^2 \end{gathered}$$

Step 2

The square of this expression is written as in mathematical form and it is expanded as 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

$$\begin{gathered} \left(a\right) \\ 1. Square the first term y^2 \\ 2. Square the last term y^2+121 \\ 3. Double their product y^2+121+2\times y\times \times 11 \\ Simplify y^2+121+22y \end{gathered}$$

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

$$\begin{gathered} \left(b\right) \\ 1. Square the first term 16x^2 \\ 2. Square the last term 16x^2+25y^2 \\ 3. Double their product 16x^2+25y^2-2\times 4x\times 5y \\ Simplify 16x^2+25y^2-40xy \end{gathered}$$