(6x%5E2%2B5xy-7y%5E2).jpeg "(3x-y)(6x^2+5xy-7y^2)")
Expanding the Expression (3x-y)(6x^2+5xy-7y^2)
This article will guide you through expanding the expression (3x-y)(6x^2+5xy-7y^2). This involves applying the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for binomial multiplication.
Applying the Distributive Property
We can expand the expression by multiplying each term in the first binomial (3x-y) by each term in the second binomial (6x^2+5xy-7y^2).
Let's break it down step by step:
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Multiply 3x by each term in the second binomial:
- 3x * 6x^2 = 18x^3
- 3x * 5xy = 15x^2y
- 3x * -7y^2 = -21xy^2
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Multiply -y by each term in the second binomial:
- -y * 6x^2 = -6x^2y
- -y * 5xy = -5xy^2
- -y * -7y^2 = 7y^3
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Combine all the terms:
- 18x^3 + 15x^2y - 21xy^2 - 6x^2y - 5xy^2 + 7y^3
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Simplify by combining like terms:
- 18x^3 + 9x^2y - 26xy^2 + 7y^3
The Final Result
Therefore, the expanded form of (3x-y)(6x^2+5xy-7y^2) is 18x^3 + 9x^2y - 26xy^2 + 7y^3.