# NCERT Solutions Class 8 Mathematics Solutions for Exercise 9.5 in Chapter 9 - Algebraic Expressions and Identities

Question 13 Exercise 9.5

\text { Using } a^{2}-b^{2}=(a+b)(a-b), \text { find }

\text { (i) } 51^{2}-49^{2}

\text { (ii) }(1.02)^{2}-(0.98)^{2}

\text { (iii) } 153^{2}-147^{2}

\text { (iv) } 12.1^{2}-7.9^{2}

\begin{aligned} &\text { i) } 51^{2}-49^{2}\\ &\begin{array}{l} =(51+49)(51-49) \\ =100 \times 2 \\ =200 \end{array} \end{aligned}

\begin{aligned} &\text { ii) }(1.02)^{2}-(0.98)^{2}\\ &\begin{array}{l} =(1.02+0.98)(1.02-0.98) \\ =2 \mathrm{x} 0.04 \\ =0.08 \end{array} \end{aligned}

\begin{aligned} &\text { iii) } 153^{2}-147^{2}\\ &\begin{array}{l} =(153+147)(153-147) \\ =300 \times 6 \\ =1800 \end{array} \end{aligned}

\begin{aligned} &\text { iv) } 12.1^{2}-7.9^{2}\\ &=(12.1+7.9)(12.1-7.9)\\ &=20 \times 4.2=84 \end{aligned}

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