Exercise 5 G
Question 1
Find the following products :
(i) (x+2)(x-2)
Sol :
(ii) $(d-8)(d+8)$
Sol :
(iii) $(5+9 m)(5-9 m)$
Sol :
(iv) $\left(x^{2}-y^{2}\right)\left(x^{2}+y^{2}\right)$
Sol :
(v) $\left(\frac{2}{5} a b-c\right)\left(\frac{2}{5} a b+c\right)$
Sol :
(vi) $\left(\frac{2}{b}-\frac{5}{c}\right)\left(\frac{2}{b}+\frac{5}{c}\right)$
Sol :
Question 2
(i) $(a+1)(a-1)\left(a^{2}+1\right)$
Sol :
(ii) $(a+x)(a-x)\left(a^{2}+x^{2}\right)$
Sol :
(iii) $\left(x-\frac{1}{x}\right)\left(x+\frac{1}{x}\right)\left(x^{2}+\frac{1}{x^{2}}\right)$
Sol :
(iv) $\left(x^{3}-\frac{1}{x^{3}}\right)\left(x^{3}+\frac{1}{x^{3}}\right)\left(x^{6}+\frac{1}{x^{6}}\right)$.
Sol :
Question 3
Using the identity for difference of two squares, find the values of :
(i) $18 \times 22$
(ii) $101 \times 99$
(iii) $(84)^{2}-(76)^{2}$
(iv) $(203)^{2}-(197)^{2}$
Sol :
Question 4
Find the value of $x$, if :
(i) $13 x=(58)^{2}-(45)^{2}$
(ii) $24 x=(99)^{2}-(87)^{2}$
Sol :
Question 5
Simplify :
(i) $179 \times 179-21 \times 21$
(ii) $1.62 \times 1.62-0.38 \times 0.38$
(iii) $\frac{297 \times 297-203 \times 203}{94}$ [Hint. $\left.94=297-203\right]$
(iv) $\frac{23.71 \times 23.71-16.29 \times 16.29}{0.742}$.
Sol :
Multiple Choice Questions (MCQs)
Question 6
$(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right)\left(1+x^{8}\right)(1-x)$
(a) $1+x^{16}$
(b) $1-x^{16}$
(c) $x^{16}-1$
(d) $x^{8}+1$
Sol :
Question 7
$\frac{4.359 \times 4.359-1.641 \times 1.641}{4.359-1.641}=$ ?
(a) $6.3$
(b) 6
(c) $3.2$
(d) $4.6$
Sol :
High Order Thinking Skills (HOTS)
Question 8
$\frac{3.7 \times 3.7+2.3 \times 2.3+2 \times 3.7 \times 2.3}{4.6 \times 4.6-3.4 \times 3.4}$ equals
(a) $3 \frac{3}{4}$
(b) $4 \frac{3}{4}$
(c) $3 \frac{1}{4}$
(d) $3 \frac{1}{2}$
Sol :
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