Question : The value of $(2a+b)^{2}-(2a-b)^{2}$ is:
Option 1: $8ab$
Option 2: $–8ab$
Option 3: $8a^{2}+2b^{2}$
Option 4: $8a^{2}–2b^{2}$
Answer (1)
25th Jan, 2024
Correct Answer: $8ab$
Solution :
Given: $(2a+b)^{2}–(2a–b)^{2}$
We know that: $a^2-b^2=(a+b)(a-b)$
Applying this to expression, we have,
= $(2a+b+2a-b)(2a+b-2a+b)$
= $(4a)(2b)$
= $8ab$
Hence, the correct answer is $8ab$.
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