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: $1$
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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Question : Simplify the given expression. $(1 - 2x)^2 - (1 + 2x)^2$
Option 1: $8x$
Option 2: $-8x$
Option 3: $-(2 + 8x^2)$
Option 4: $2 + 8x^2$
Question : What the least value should be added to 2505 so that it becomes a perfect square?
Option 1: 5
Option 2: 20
Option 3: 70
Option 4: 96
Question : What smallest value must be added to 508, so that the resultant is a perfect square?
Option 1: 4
Option 2: 9
Option 3: 18
Option 4: 21
Question : What is the smallest value that must be added to 709, so that the resultant is a perfect square?
Option 1: 8
Option 2: 12
Option 3: 20
Option 4: 32
Question : One of the factors of the expression $4\sqrt{3}x^{2}+5x-2\sqrt{3}$ is:
Option 1: $4x+\sqrt{3}$
Option 2: $4x+3$
Option 3: $4x-3$
Option 4: $4x-\sqrt{3}$
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