In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

# Ex.2.5 Q1 Polynomials Solution - NCERT Maths Class 9

Go back to  'Ex.2.5'

## Question

Use suitable identities to find the following products:

(i) \begin{align}(x+4)(x+10)\end{align}

(ii) \begin{align}(x+8)(x-10)\end{align}

(iii) \begin{align}(3 x+4)(3 x-5)\end{align}

(iv) \begin{align}\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)\end{align}

(v) \begin{align}(3-2 x)(3+2 x)\end{align}

Video Solution
Polynomials
Ex 2.5 | Question 1

## Text Solution

​​​​​​Reasoning:

Identities: \begin{align}(x+a)(x+b)&=x^{2}+(a+b) x+a b \\ (a+b)(a-b)&=a^{2}-b^{2}\end{align}

Steps:

\begin{align}\text{(i)}\;\;(x+4)(x+10)\end{align}

Identity: \begin{align}(x+a)(x+b)=x^{2}+(a+b) x+a b\end{align}

Here \begin{align}\text{a} = {4}, \text{b} = 10\end{align}

\begin{align}&(x+4)(x+10) \\&=x^{2}+(4+10) x+4 \times 10 \\ &=x^{2}+14 x+40 \end{align}

\begin{align}\text{(ii)}\;\;(x+8)(x-10)\end{align}

Identity: \begin{align}(x+a)(x+b)=x^{2}+(a+b) x+a b\end{align}

Here $$a =8, b=-10$$

\begin{align}&(x+8)(x-10) \\&=x^{2}+(8-10) x+(8)(-10) \\ &=x^{2}-2 x-80 \end{align}

\begin{align}\text{(iii)}\;\;(3 x+4)(3 x-5)\end{align}

Identity: \begin{align}(x+a)(x+b)=x^{2}+(a+b) x+a b\end{align}

Here \begin{align}x \rightarrow 3 x, a=4, b=-5\end{align}

\begin{align}&(3 x+4)(3 x-5) \\&=(3 x)^{2}+(4-5)(3 x)+(4)(-5) \\ &=9 x^{2}-3 x-20 \end{align}

(iv) \begin{align}\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)\end{align}

Identity: \begin{align}(a+b)(a-b)=a^{2}-b^{2}\end{align}

Here \begin{align}a=y^{2}, b=\frac{3}{2}\end{align}

\begin{align}&\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right) \\&=\left(y^{2}\right)^{2}-\left(\frac{3}{2}\right)^{2} \\ &=y^{4}-\frac{9}{4} \end{align}

(v) \begin{align}(3-2 x)(3+2 x) \end{align}

Identity: \begin{align}(a+b)(a-b)=a^{2}-b^{2}\end{align}

Here \begin{align}a=3, b=2 x\end{align}

\begin{align}&(3-2 x)(3+2 x) \\&=(3)^{2}-(2 x)^{2} \\ &=9-4 x^{2} \end{align}

Video Solution
Polynomials
Ex 2.5 | Question 1

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school