Answer

Verified

385.8k+ views

**Hint:**In this question, we are given an expression and we have been asked to factorize it. Observe the expression carefully and you will find an identity in the question. Using that identity, expand the given expression and you will have your answer.

**Formula used:**${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$

**Complete step-by-step solution:**

We are given an expression, $1 - {y^2}$ and we have to factorize the given expression. Let us see below how it can be done.

$ \Rightarrow 1 - {y^2}$ …. (given)

We can also write it as –

$ \Rightarrow {1^2} - {y^2}$

Now, if we see, both the terms are in complete squares. It reminds us of the formula ${a^2} - {b^2}$.

Let us take $a = 1$ and $b = y$.

Our formula says - ${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$.

Using the formula, we will get,

$ \Rightarrow {1^2} - {y^2} = \left( {1 + y} \right)\left( {1 - y} \right)$

**Hence, the factors of ${1^2} - {y^2}$ are $\left( {1 + y} \right)\left( {1 - y} \right)$**

**Note:**1) Here we used the word “expression” and not “equation”. This is because an equation should necessarily have the sign of “equals” (=). But here, in our case, our expression does not have the required sign. Hence, we call it “expression” and not “equation”.

2) Using the factors, we can find the value of $y$ as well. Let us expand our question and find the values.

We have already found the factors of ${1^2} - {y^2}$. They are$\left( {1 + y} \right)\left( {1 - y} \right)$. Now, we will put each factor equal to 1.

$ \Rightarrow 1 + y = 0,1 - y = 0$

Shifting the terms to the other side,

$ \Rightarrow y = - 1,y = 1$

Now, we have the values of $y$ also.

3) We can also find the values of $y$ without finding the factors. Let us see how that can be done.

The expression given to us is - $1 - {y^2}$.

Let us keep the expression equal to $0$.

$ \Rightarrow 1 - {y^2} = 0$

We will shift the variable to the other side,

$ \Rightarrow 1 = {y^2}$

Square rooting both the sides,

$ \Rightarrow \sqrt 1 = \sqrt {{y^2}} $

Therefore, $y = \pm 1$.

Recently Updated Pages

How do you evaluate cos left dfrac13pi 12 right class 10 maths CBSE

How do you rewrite the inequality left 11 2x right class 10 maths CBSE

How do you solve 4 3x 025 class 10 maths CBSE

How do you find the zeros of x3 3x2 + 6x 18 class 10 maths CBSE

Consider the following statements in respect of the class 10 maths CBSE

How do you factor 2x3 + 3x2 8x 12 class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail

Name 10 Living and Non living things class 9 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths