Question

You can use the binomial squares pattern to multiply numbers without a calculator. Say you need to square 65. Think of 65 as 60+5.Multiply (60 + 5)^2 by using the binomial squares pattern, (a + b)^2 = a^2 + 2ab + b^2 1.) Square 65 without using a calculator.2.) Which way is easier? Explain.

Answer 1

ANSWER and EXPLANATION

1) We want to find the square of 65 without using a calculator. To do this, we want to apply Binomial squares:

`(a+b)^2=a^2+2ab+b^2`

Therefore, the square of 65 is:

`\begin{gathered} 65^2=(60+5)^2=60^2+2(60)(5)+5^2 \\ \Rightarrow65^2=3600+600+25 \\ 65^2=4225 \end{gathered}`

2) Although picking the easier method is a thing of personal choice, finding the squares of numbers, especially large numbers, directly without using calculators can be difficult because then you would have to know multiplication tables of large numbers but the binomial square method is easier since there is less multiplication involved and the multiplications are broken into smaller steps.