Answered

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Derive the Equation → ( a + b )2

Sagot :

Let us calculate the area of a square

As you can see in the above figure,

The length of the square is

[tex]L=(a+b)[/tex]

The width of the square is

[tex]W=(a+b)[/tex]

Recall that the area of a square shape is given by

[tex]A=L\cdot W[/tex]

So the area of the square becomes

[tex]\begin{gathered} A=L\cdot W \\ A=(a+b)\cdot(a+b) \\ A=(a+b)^2 \end{gathered}[/tex]

Now let us draw the square again,

As you can see in the above figure,

The area of the square is

[tex]\begin{gathered} A=a^2+ab+ab+b^2 \\ A=a^2+2ab+b^2 \end{gathered}[/tex]

Therefore,

[tex](a+b)^2=a^2+2ab+b^2[/tex]

View image CarlottaH316951
View image CarlottaH316951
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