(4a%5E2-2a%2B1).jpeg "(3a+2)(4a^2-2a+1)")
Expanding the Expression: (3a + 2)(4a² - 2a + 1)
This expression represents the multiplication of two binomials: (3a + 2) and (4a² - 2a + 1). To expand this expression, we can use the distributive property or the FOIL method.
Using the Distributive Property
The distributive property states that for any numbers a, b, and c: a(b + c) = ab + ac. We can apply this property twice in this case:
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Distribute (3a + 2) over the entire second binomial: (3a + 2)(4a² - 2a + 1) = 3a(4a² - 2a + 1) + 2(4a² - 2a + 1)
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Distribute 3a and 2 individually: = (12a³ - 6a² + 3a) + (8a² - 4a + 2)
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Combine like terms: = 12a³ + 2a² - a + 2
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and it's a mnemonic device to remember the steps for multiplying two binomials:
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First: Multiply the first terms of each binomial: 3a * 4a² = 12a³
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Outer: Multiply the outer terms: 3a * 1 = 3a
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Inner: Multiply the inner terms: 2 * -2a = -4a
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Last: Multiply the last terms: 2 * 1 = 2
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Combine like terms: 12a³ + 3a - 4a + 2 = 12a³ + 2a² - a + 2
Conclusion
Both methods lead to the same expanded expression: 12a³ + 2a² - a + 2. This expression represents the product of the two binomials (3a + 2) and (4a² - 2a + 1).