(x-7)-in-standard-form.jpeg "(x+7)(x-7) In Standard Form")
Expanding (x+7)(x-7) into Standard Form
The expression (x+7)(x-7) is a product of two binomials. To write it in standard form, we need to expand the product using the distributive property or the FOIL method.
Using the Distributive Property
The distributive property states that a(b + c) = ab + ac. We can apply this property twice to expand the expression:
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First, distribute the (x+7) term: (x+7)(x-7) = x(x-7) + 7(x-7)
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Next, distribute the x and 7 terms: x(x-7) + 7(x-7) = x² - 7x + 7x - 49
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Combine like terms: x² - 7x + 7x - 49 = x² - 49
Using the FOIL Method
The FOIL method stands for First, Outer, Inner, Last. It provides a systematic way to multiply two binomials:
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First: Multiply the first terms of each binomial: x * x = x²
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Outer: Multiply the outer terms of the binomials: x * -7 = -7x
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Inner: Multiply the inner terms of the binomials: 7 * x = 7x
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Last: Multiply the last terms of each binomial: 7 * -7 = -49
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Combine like terms: x² - 7x + 7x - 49 = x² - 49
Conclusion
Both methods lead to the same result. The standard form of (x+7)(x-7) is x² - 49. This is a special case known as the difference of squares pattern, where (a+b)(a-b) = a² - b².