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Question

If P = 7a - [6b - {9a - (5c + 12b) + 5c - 5 (3a - 5b)}]
and Q = 6a - [15b - {8a - (4c + 11b) + 4c}].
then (16P + 7Q) is equal to:

A
112a
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B
118a
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C
114a-294b
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D
124a
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Solution

The correct option is D 114a-294b
Given
P=7a[6b{9a(5c+12b)+5c5(3a5b)}]
=7a[6b{9a5c12b+5c15a+25b}]
=7a[6b(6a+13b)]
=7a[6b+6a13b]
=7a[6a7b]
=7a6a+7b
=a7b
Q=6a[15b{8a(4c+11b)+4c}]
=6a[15b{8a4c11b+4c}]
=6a[15b{8a11b}]
=6a[15b8a+11b]
=6a[26b8a]
=14a26b
16P+7Q
=16(a7b)+7(14a26b)
=16a112b+98a182b
=114a294b

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