Question

Expand the following:

(3x – 5y)³

Answer 1

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