Question 84 (xiii)

Simplify

$(s^{2} t + t q^{2})^{2} - (2 s t q)^{2}$

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Solution

We have, $(s^{2} t + t q^{2})^{2} - (2 s t q)^{2}$
$= (s^{2} t)^{2} + (t q^{2})^{2} + 2 \times s^{2} t \times t q^{2} - 4 s^{2} t^{2} q^{2} = s^{4} t^{2} + t^{2} q^{4} - 2 s^{2} t^{2} q^{2}$

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Simplify

$(s^{2} t + t q^{2})^{2} - (2 s t q)^{2}$

Question 58
${(\frac{5}{8})}^{9} \div {(\frac{5}{8})}^{4} = {(\frac{5}{8})}^{4}$

Question 84 (viii)

Simplify

$(a b - c)^{2} + 2 a b c$

Question 84 (xii)

Simplify

$(p q - q r)^{2} + 4 p q^{2} r$

Question 84 (x)

Simplify

$(b^{2} - 49) (b + 7) + 343$

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