(x+y)^3-(x-y)^3 Can Be Factorized As

Jasonbradley

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Jun 17, 2024

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Factoring (x+y)^3 - (x-y)^3

The expression (x+y)^3 - (x-y)^3 can be factored using the difference of cubes formula. This formula states that:

a³ - b³ = (a - b)(a² + ab + b²)

To apply this to our expression, we let:

• a = (x+y)
• b = (x-y)

Substituting these into the difference of cubes formula, we get:

(x+y)³ - (x-y)³ = [(x+y) - (x-y)][(x+y)² + (x+y)(x-y) + (x-y)²]

Now, we simplify each part:

• [(x+y) - (x-y)] = 2y
• [(x+y)² + (x+y)(x-y) + (x-y)²] = (x² + 2xy + y²) + (x² - y²) + (x² - 2xy + y²) = 3x² + y²

Therefore, the factored form of (x+y)³ - (x-y)³ is:

(x+y)³ - (x-y)³ = 2y(3x² + y²)

Key Points:

• The difference of cubes formula is a powerful tool for factoring expressions of this type.
• Recognizing the pattern of cubes allows you to apply the formula efficiently.
• Simplifying the expression after applying the formula is crucial to obtain the final factored form.