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प्रश्न
Factorise the following:
16(3x + y)3 – 24(3x + y)
योग
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उत्तर
Given expression: 16(3x + y)3 – 24(3x + y)
Step 1: Factor out the common factor 8(3x + y) from both terms:
16(3x + y)3 – 24(3x + y)
= 8(3x + y)[2(3x + y)2 – 3]
Step 2: Express inside the bracket explicitly:
= 8(3x + y)[2(3x + y)2 – 3]
Step 3: Optionally, expand (3x + y)2 = 9x2 + 6xy + y2:
= 8(3x + y)[2(9x2 + 6xy + y2) – 3]
= 8(3x + y)(18x2 + 12xy + 2y2 – 3)
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