Question

Code.

Answer 1

Answer:

$(a + b)^2=(a+b)(a+b)=(a_{1}+b_{1})(a_{2}+b_{2})$

$a_{1}=a_{2}=a \text{ and } b_{1}=b_{2}=b$

I've done this way to make it easier to understand:

Using the distributive property, multipliying $a_{1} \text{ and } a_{2}=a^2$, $a_{1} \text{ and } b_{2}=ab$,

$b_{1} \text{ and } a_{2}=ab$, and $b_{1} \text{ and } b_{2}=b^2$:

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

It is the same for $(a -b)^2$

$(a -b)^2=(a-b)(a-b)=a^2-2ab+b^2$

and $(a - b)(a + b)$

$(a - b)(a + b)=a^2+ab-ba-b^2=a^2-b^2$