Square and Product of Binomials

Suppose your class teacher gives you an activity of cutting different shapes from a paper.

And, you cut a paper in square shape which has side $x$ and area $x^2$.

Then, you cut two papers in rectangular shape which has sides $x,y$.

And, after some time you cut different paper in square shape of side y with an area of $y^2$.

Now, your teacher tells you to join these papers in such a way that it makes a square of side $(x+y)$.

And, you try to find the area of this square from the area of the small sheets.

So, the area of the new square shape sheet of side $(x+y)$ is $(x+y{)}^2$.

Then, your teacher explains to you that this is a identity of the algebraic functions.

Therefore let’s discuss the identities of the algebraic functions more clearly.

The identities are obtained from the multiplications of a binomial by another binomial.

Let’s consider the product as $(a+b{)}^2$

So, the multiplication from the distributive law is shown above.

Then, after simplification we get the identity.

So, the first identity is given in the figure.

Similarly, if we have two binomials as $(a-b{)}^2$

We can find their product, using distributive law as shown above.

And finally we get another algebraic identity.

Now, let us consider the multiplication of two binomials as $(a+b)(a-b)$.

Then, from the distributive law we can find the multiplication.

So, the third identity is as given in the figure.

Revision

We have three standard identities, first is as shown in the figure.

Second standard identity is the $(a-b{)}^2$ one given in the figure.

And third standard identity is the product of $(a-b)$ and $(a+b)$.

The End