Abbreviated Multiplication Formulas

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What is the abbreviated multiplication formula for the square of a sum (a + b)?
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(a + b)^2 = a^2 + 2ab + b^2
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What is the abbreviated multiplication formula for the square of a difference (a - b)?
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(a - b)^2 = a^2 - 2ab + b^2
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What is the abbreviated multiplication formula for the difference of squares?
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a^2 - b^2 = (a + b)(a - b)
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What is the formula for the cube of a sum (a + b)?
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(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
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What is the formula for the cube of a difference (a - b)?
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(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
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How does the formula for the square of a sum differ from the square of a difference?
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In the square of a sum, the middle term is '+', whereas in the square of a difference, it is '-'.
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What is the expanded form of (x + y)^2?
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x^2 + 2xy + y^2
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What is the expanded form of (x - y)^2?
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x^2 - 2xy + y^2
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What is the factorized form of x^2 - 9?
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(x + 3)(x - 3)
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How do you factor the expression a^2 - b^2?
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It can be factored into (a + b)(a - b).
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What does the term 'abbreviated multiplication formulas' refer to?
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They are shortcuts used to simplify the process of expanding polynomial expressions.
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What is the significance of the middle term in the formulas for squares?
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The middle term results from the product of both terms being doubled in the squares of sums or differences.
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What is the expanded form of (m + n)^3?
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m^3 + 3m^2n + 3mn^2 + n^3
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What is the key feature of the difference of squares formula?
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It results in a binomial expression with two factors: (a + b) and (a - b).
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Can the formula (a + b)^2 be used to solve (x + y + z)^2 directly?
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No, (x + y + z)^2 is not directly solved by (a + b)^2; it requires additional steps.
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