(-2x%2B3).jpeg "(5x^2-4x+6)(-2x+3)")
Expanding the Expression: (5x^2 - 4x + 6)(-2x + 3)
This article will explore how to expand the given expression by applying the distributive property.
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 mathematical terms, it can be represented as:
a(b + c) = ab + ac
Applying the Distributive Property
To expand (5x^2 - 4x + 6)(-2x + 3), we can distribute each term of the first polynomial to each term of the second polynomial:
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Distribute -2x:
- (-2x)(5x^2) = -10x^3
- (-2x)(-4x) = 8x^2
- (-2x)(6) = -12x
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Distribute 3:
- (3)(5x^2) = 15x^2
- (3)(-4x) = -12x
- (3)(6) = 18
Combining Like Terms
Now, we combine the terms with the same exponents:
-10x^3 + 8x^2 + 15x^2 -12x - 12x + 18
The final expanded form of the expression is:
-10x^3 + 23x^2 - 24x + 18
Conclusion
By applying the distributive property and combining like terms, we have successfully expanded the expression (5x^2 - 4x + 6)(-2x + 3) into a simplified polynomial: -10x^3 + 23x^2 - 24x + 18. This process is essential in various mathematical operations, such as solving equations and simplifying expressions.