(x%2B8).jpeg "(x-1)(x+8)")
Factoring and Expanding (x-1)(x+8)
This expression represents the product of two binomials: (x-1) and (x+8). We can work with it in two ways:
Expanding the Expression
To expand the expression, we use the distributive property (also known as FOIL):
First: x * x = x² Outer: x * 8 = 8x Inner: -1 * x = -x Last: -1 * 8 = -8
Now, combine the terms:
x² + 8x - x - 8 = x² + 7x - 8
This is the expanded form of the expression.
Factoring the Expression
If we start with the expanded form (x² + 7x - 8), we can factor it back into the original binomials. Here's how:
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Find two numbers that add up to the coefficient of the middle term (7) and multiply to the constant term (-8). In this case, the numbers are 8 and -1.
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Rewrite the middle term using these two numbers. x² + 8x - x - 8
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Group the terms and factor out the greatest common factor (GCF) from each group. x(x + 8) - 1(x + 8)
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Notice that both terms have a common factor of (x + 8). Factor it out: (x + 8)(x - 1)
This gives us the original factored form: (x - 1)(x + 8)
Conclusion
Both expanding and factoring the expression (x-1)(x+8) involve understanding the relationships between binomials and their products. By applying the distributive property and factoring techniques, we can work with this expression in different forms depending on the context of the problem.