Simplify:
i) ${(a^{2} - b^{2})}^{2}$
ii) ${(2 x + 5)}^{2} - {(2 x - 5)}^{2}$

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Solution

$(i) (a^{2} - b^{2})^{2} = (a^{2})^{2} - 2. a^{2} . b^{2} + (b^{2})^{2}$
$= a^{4} - 2 a^{2} b^{2} + b^{4}$
$(i i) (2 x + 5)^{2} - (2 x - 5)^{2}$
$= (2 x)^{2} + 2 \times 2 x \times 5 + 5^{2} - {(2 x)^{2} - 2 \times 2 x \times 5 + (5)^{2}}$
$= 4 \times 2 x \times 5$
$= 40 x$

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Question 4(ii)
Simplify:
$(2 x + 5)^{2} - (2 x - 5)^{2}$

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