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

Question 8 Exercise 9.5

Simplify.

(i) \left(a^{2}-b^{2}\right)^{2}

(ii) (2 x+5)^{2}-(2 x-5)^{2}

\text { (iii) }(7 \mathrm{m}-8 \mathrm{n})^{2}+(7 \mathrm{m}+8 \mathrm{n})^{2}

(\mathbf{i v})(4 \mathbf{m}+\mathbf{5} \mathbf{n})^{2}+(5 \mathbf{m}+\mathbf{4} \mathbf{n})^{2}

(v)(2.5 p-1.5 q)^{2}-(1.5 p-2.5 q)^{2}

\text { (vi) }(a b+b c)^{2}-2 a b^{2} c

\text { (vii) }\left(\mathrm{m}^{2}-\mathrm{n}^{2} \mathrm{m}\right)^{2}+2 \mathrm{m}^{3} \mathrm{n}^{2}

\text { i) }\left(a^{2}-b^{2}\right)^{2}=a^{4}+b^{4}-2 a^{2} b^{2}

\begin{aligned} &\text { ii) }(2 x+5)^{2}-(2 x-5)^{2}\\ &=4 x^{2}+20 x+25-\left(4 x^{2}-20 x+25\right)\\ &=4 x^{2}+20 x+25-4 x^{2}+20 x-25\\ &=40 \mathrm{x} \end{aligned}

\begin{aligned} &\text { iii) }(7 \mathrm{m}-8 \mathrm{n})^{2}+(7 \mathrm{m}+8 \mathrm{n})^{2}\\ &=49 \mathrm{m}^{2}-112 \mathrm{mn}+64 \mathrm{n}^{2}+49 \mathrm{m}^{2}+112 \mathrm{mn}+49 \mathrm{n}^{2}\\ &=98 \mathrm{m}^{2}+128 \mathrm{n}^{2} \end{aligned}

\begin{aligned} &\text { iv) }(4 \mathrm{m}+5 \mathrm{n})^{2}+(5 \mathrm{m}+4 \mathrm{n})^{2}\\ &=16 \mathrm{m}^{2}+40 \mathrm{mn}+25 \mathrm{n}^{2}+25 \mathrm{m}^{2}+40 \mathrm{mn}+16 \mathrm{n}^{2}\\ &=41 \mathrm{m}^{2}+80 \mathrm{mn}+41 \mathrm{n}^{2} \end{aligned}

\begin{aligned} &\text { v) }(2.5 p-1.5 q)^{2}-(1.5 p-2.5 q)^{2}\\ &=6.25 \mathrm{p}^{2}-7.5 \mathrm{pq}+2.25 \mathrm{q}^{2}-2.25 \mathrm{p}^{2}+7.5 \mathrm{pq}-6.25 \mathrm{q}^{2}\\ &=4 p^{2}-4 q^{2} \end{aligned}

\begin{aligned} &\text { vi) }(a b+b c)^{2}-2 a b^{2} c\\ &=a^{2} b^{2}+2 a b^{2} c+b^{2} c^{2}-2 a b^{2} c\\ &=a^{2} b^{2}+b^{2} c^{2} \end{aligned}

\begin{aligned} &\text { vii) }\left(\mathrm{m}^{2}-\mathrm{n}^{2} \mathrm{m}\right)^{2}+2 \mathrm{m}^{3} \mathrm{n}^{2}\\ &\begin{array}{l} =\mathrm{m}^{4}-2 \mathrm{m}^{3} \mathrm{n}^{2}+\mathrm{m}^{2} \mathrm{n}^{4}+2 \mathrm{m}^{3} \mathrm{n}^{2} \\ =\mathrm{m}^{4}+\mathrm{m}^{2} \mathrm{n}^{4} \end{array} \end{aligned}

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