(3x-5).jpeg "(2x+9)(3x-5)")
Expanding the Expression (2x+9)(3x-5)
In mathematics, expanding an expression means writing it in a simpler form without parentheses. We can achieve this by applying the distributive property.
The Distributive Property
The distributive property states that:
a(b+c) = ab + ac
This means we can multiply a term outside parentheses by each term inside the parentheses.
Expanding (2x+9)(3x-5)
Let's apply this to our expression:
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Multiply the first term of the first parentheses by each term of the second parentheses:
- (2x)(3x) = 6x²
- (2x)(-5) = -10x
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Multiply the second term of the first parentheses by each term of the second parentheses:
- (9)(3x) = 27x
- (9)(-5) = -45
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Add all the terms together:
- 6x² - 10x + 27x - 45
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Combine like terms:
- 6x² + 17x - 45
Therefore, the expanded form of (2x+9)(3x-5) is 6x² + 17x - 45.
Conclusion
By using the distributive property, we successfully expanded the expression (2x+9)(3x-5) and obtained a simplified polynomial form. This process is fundamental in algebraic manipulation and helps us solve various mathematical problems.