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 $4cd$.
Related Questions
Question : Simplify the given expression $\frac{3\left(\sin ^4 z-\cos ^4 z+1\right)}{\sin ^2 z}$
Question : Simplify the expression:
$\frac{a+b}{a-b} \div \frac{(a+b)^2}{\left(a^2-b^2\right)}$
$\frac{a+b}{a-b} \div \frac{(a+b)^2}{\left(a^2-b^2\right)}$
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