Question

Evaluate using identity (8.7) ^2 -(1.3) ^2​

Answer 1

Let us know some identity formulae first:

• $(a+b)^{2}=a^{2}+2ab+b^{2}$

• $(a-b)^{2}=a^{2}-2ab+b^{2}$

• $a^{2}+b^{2}=(a+b)^{2}-2ab$

• $a^{2}+b^{2}=(a-b)^{2}+2ab$

• $a^{2}-b^{2}=(a+b)(a-b)$

Step-by-step explanation:

Now, $(8.7)^{2}-(1.3)^{2}$

The identity formula $\boxed{a^{2}-b^{2}=(a+b)(a-b)}$ is used here.

$\Rightarrow (8.7+1.3)(8.7-1.3)$ where we assume $a=8.7$ and $b=1.3$

$\Rightarrow (10.0)(7.4)$

$\Rightarrow \bold{74}$

Answer:

Thus $(8.7)^{2}-(1.3)^{2}=74$