How to Multiply Algebraic Expressions
In algebra, it is relatively easy to multiply powers of numbers. Just as 2 x 2 is the second power of two (or square of 2), a x a is the second power of a, written as a^2. If there are multiple variables, you would multiply by combining like terms: abaab = a^3b^2. In algebraic expressions with parentheses, we know that x(a + b) = xa + xb. One can use this principle when multiplying algebraic expressions.
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Instructions
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When multiplying an algebraic expression with two terms, multiply the second factor by each of the terms in the first factor. Add the two products to get the final product.
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Take this sample problem: (a - x)(b + y).
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Multiply (b + y) by the terms of the first factor, a and -x. So a(b + y) + -x(b + y).
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Multiply out the parentheses: ab + ay - bx -xy. This is the final answer.
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Understand that, since the order of operations is irrelevant in multiplication, it does not matter in which order you write the factors. (b + y)(a - x) = b(a -x) + y(a -x) = ab - bx + ay - xy. The answer is the same.
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Know that, for algebraic expressions with differing coefficients in the first terms, the process is still the same. Take this sample problem: (3x - 2y)(2x - 3y).
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Take the second factor and multiply by each term in the first factor. So 3x(2x - 3y) + -2y(2x - 3y).
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Multiply out the parentheses: 6x^2 - 9xy - 4xy + 6y^2.
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Combine like terms: 6x^2 - 13xy + 6y^2. This is the final answer.
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Apply this method when multiplying expressions with three terms. Take an example problem: (x - a)(x^2 + 2ax + a^2).
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Take the second factor and multiply it by each term in the first factor. So x(x^2 + 2ax + a^2) - a(x^2 + 2ax + a^2).
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Multiply out the parentheses: x^3 + 2ax^2 + a^2x - ax^2 - 2a^2x - a^3.
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Combine like terms: x^3 + ax^2 - a^2x - a^3. This is the final answer.
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