Chapter 5.6, Problem 19OE

To determine

To find: The square of 21 by thinking of it as ${\left(20+1\right)}^{\text{2}}$ .

Answer to Problem 19OE

The square of 21 by thinking of it as ${\left(20+1\right)}^{\text{2}}$ is 441.

Explanation of Solution

Given information:

The given square is ${21}^2={\left(20+1\right)}^{\text{2}}$ .

Formula used:

The expansion of ${\left(a-b\right)}^{\text{2}}=a^2-2ab+b^2$ where $a^2-2ab+b^2$ is a trinomial (3 terms polynomial).

The expansion of ${\left(a+b\right)}^{\text{2}}=a^2+2ab+b^2$ where $a^2+2ab+b^2$ is a trinomial.

Calculations:

The square of 21 can be written as ${21}^2={\left(20+1\right)}^{\text{2}}$

Now, substituting $a=20$ and $b=1$ in expression ${\left(a+b\right)}^{\text{2}}=a^2+2ab+b^2$

  $\Rightarrow {\left(20+1\right)}^{\text{2}}={\left(20\right)}^2+2\left(20\right)\left(1\right)+{\left(1\right)}^2$

  $\Rightarrow {\left(20+1\right)}^{\text{2}}=400+40+1$

  $\Rightarrow {21}^{\text{2}}=441$

Thus, the square of 21 by thinking of it as ${\left(20+1\right)}^{\text{2}}$ is 441.

Conclusion:

The square of 21 by thinking of it as ${\left(20+1\right)}^{\text{2}}$ is 441.