Which of the following is equivalent to 2p(a – b) + 3q(5a – 5b) + 4r(2b – 2a)? A. (a – b)(2p + 3q – 4r) B. (b – a)(2p + 15q – 8r) C. (b – a)(2p – 15q + 8r) D. (a – b)(2p + 15q – 8r)
Equivalent form of 2p(a − b) + 3q(5a − 5b) + 4r(2b − 2a)
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Which of the following is equivalent to 2p(a – b) + 3q(5a – 5b) + 4r(2b – 2a)? A. (a – b)(2p + 3q – 4r) B. (b – a)(2p + 15q – 8r) C. (b – a)(2p – 15q + 8r) D. (a – b)(2p + 15q – 8r)
To simplify the expression (2p(a – b) + 3q(5a – 5b) + 4r(2b – 2a)), we can factor each term:
1. (2p(a – b)) is already factored.
2. (3q(5a – 5b) = 3q cdot 5(a – b) = 15q(a – b)).
3. (4r(2b – 2a) = 4r cdot -2(a – b) = -8r(a – b)).
Now we can combine these:
[
2p(a – b) + 15q(a – b) – 8r(a – b) = (2p + 15q – 8r)(a – b).
]
This shows that the expression can be rewritten as ((a – b)(2p + 15q – 8r)).
Therefore, the correct answer is D. (a – b)(2p + 15q – 8r).