(x%5E2-3x%2B6).jpeg "(5x+2)(x^2-3x+6)")
Expanding the Expression: (5x+2)(x^2-3x+6)
This article explores the process of expanding the given expression: (5x+2)(x^2-3x+6). We will use the distributive property (also known as FOIL) to achieve this.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In simpler terms, we can distribute the first term of the first binomial to every term in the second binomial, then repeat the process for the second term of the first binomial.
Expanding the Expression
Let's apply this to our given expression:
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Distribute the first term (5x) of the first binomial:
- (5x)(x^2) = 5x^3
- (5x)(-3x) = -15x^2
- (5x)(6) = 30x
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Distribute the second term (2) of the first binomial:
- (2)(x^2) = 2x^2
- (2)(-3x) = -6x
- (2)(6) = 12
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Combine all the resulting terms:
- 5x^3 - 15x^2 + 30x + 2x^2 - 6x + 12
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Simplify by combining like terms:
- 5x^3 - 13x^2 + 24x + 12
Conclusion
Therefore, the expanded form of the expression (5x+2)(x^2-3x+6) is 5x^3 - 13x^2 + 24x + 12. This process demonstrates the power of the distributive property in simplifying and manipulating algebraic expressions.