Question : The term that should be added to ($4x^2+8x$) so that the resulting expression be a perfect square, is:
Option 1: $2$
Option 2: $4$
Option 3: $2x$
Option 4: $1$
Answer (1)
22nd Jan, 2024
Correct Answer: $4$
Solution :
$4x^2+8x$ = $(2x)^2+2×(2x)×2$
Adding $4$ on both sides then use identity: $(a + b)^2 = a^2 + b^2 + 2ab$
$4x^2+8x+4$ = $(2x)^2+2×(2x)×2+4$ = $(2x+2)^2$
Thus, $4$ is to be added to $4x^2+8x$ to make it a perfect square.
Hence, the correct answer is $4$.
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