Chapter 7.3, Problem 1E

To determine

To explain: How to use square of a binomial pattern.

Answer to Problem 1E

The square of a binomial pattern ${(a+b)}^2$ is $a^2+2ab+b^2$ .

Explanation of Solution

Given information:

The given polynomial is, say, ${(a+b)}^2$ , that is, square of a binomial pattern.

Calculation:

Binomials can be squared by FOIL method or tabular method. But the shortcut is to just follow these 3 steps:

1. Square the first term of the binomial,

  ${(a)}^2=a^2$

2. Multiply the first and the last term of the binomial and then multiply that quantity by 2,

  $[(a)\times (b)]\times 2=2ab$

3. Square the last term of the binomial,

  ${(b)}^2=b^2$

4. Add all these terms and the required square of the binomial is,

  ${(a+b)}^2$ $=a^2+2ab+b^2$ .