Question : Simplify the expression: $(c+d)^2-(c-d)^2$
Option 1: $4cd$
Option 2: $\left(c^2+d^2\right)$
Option 3: $2\left(c^2+d^2\right)$
Option 4: $2cd$
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Correct Answer: $4cd$
Solution : We know that: $(a-b)^2=a^2+b^2-2ab$ So, $(c+d)^2-(c-d)^2$ $= c^2+d^2+2cd-(c^2+d^2-2cd)$ $= 4cd$ Hence, the correct answer is $4cd$.
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Question : Simplify the following expression: $\frac{\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2}{b^2-c^2}$
Option 1: $3a^2$
Option 2: $4a^2$
Option 3: $5a^2$
Option 4: $2a^2$
Question : Simplify the given expression $\frac{3\left(\sin ^4 z-\cos ^4 z+1\right)}{\sin ^2 z}$
Option 1: 9
Option 2: 2
Option 3: 4
Option 4: 6
Question : Simplify the expression: $\frac{a+b}{a-b} \div \frac{(a+b)^2}{\left(a^2-b^2\right)}$
Option 1: $–1$
Option 2: $(a + b)$
Option 3: $0$
Option 4: $1$
Question : Simplify the given expression $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$
Option 1: 40
Option 2: 50
Option 3: 60
Option 4: 30
Question : Simplify the given expression. $40 \times 7-2 \times\left(11^3 \div 11\right) \div 22+30$
Option 1: 297
Option 2: 298
Option 3: 300
Option 4: 299
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