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प्रश्न
Expand the following:
(3x – 5y)3
बेरीज
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उत्तर
Step 1: Apply the binomial formula
To expand the expression (3x – 5y)3, we use the binomial difference formula for a cube:
(a – b)3 = a3 – 3a2b + 3ab2 – b3
Step 2: Substitute variables
We substitute a = 3x and b = 5y into the formula:
(3x – 5y)3 = (3x)3 – 3(3x)2(5y) + 3(3x)(5y)2 – (5y)3
Step 3: Simplify terms
Simplify each term in the expression:
(3x)3 = 27x3
3(3x)2(5y) = 3(9x2)(5y) = 135x2y
3(3x)(5y)2 = 3(3x)(25y2) = 225xy2
(5y)3 = 125y3
Step 4: Combine the simplified terms
Combining the simplified terms yields the final expanded form:
(3x – 5y)3 = 27x3 – 135x2y + 225xy2 – 125y3
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