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Algebraic Expression

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Question

Select a suitable identity and the product of the following equation
$(2 b - a) (2 b + c)$ is $4 b^{2} - 2 a b + 2 b c - a c$

A

True

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B

False

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Solution

The correct option is A True
We multiply the given expression $(2 b - a) (2 b + c)$ as shown below:

$(2 b - a) (2 b + c) = 2 b (2 b + c) - a (2 b + c) = (2 b \times 2 b) + (2 b \times c) + (- a \times 2 b) + (- a \times c) = 4 b^{2} + 2 b c - 2 a b - a c$

Hence, $(2 b - a) (2 b + c) = 4 b^{2} - 2 a b + 2 b c - a c$ .

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