(Solved) What does it mean to "find the product" and "factor out the common factor" in pre-calc?

smokeyd

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11 years ago

What does it mean to "find the product" and "factor out the common factor" in pre-calc?

My pre-calc packet asks me to "find the product" and "factor out the common factor".. and I am a bit confused.

Here are some of the questions that tell me to "find the product":
1. (?x + ?y)(?x - ?y) --------- the ?'s are square roots.
2. (5 + ?x)(5 - ?x)

Here are some of the questions that tell me to "factor out the common factor":
1. 3x + 6
2. 3x(x + 2) - 4(x + 2)
3. 2x^2 - 6x

Can someone explain them to me? Thanks

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irina

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firebucks74

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11 years ago

Multiply each term times the other terms.
SO (a+b)(a-b) = (a+b)a - (a+b)b
= a*a + b*a - (a*b + b*b)
= a*a + b*a - a*b - b*b
= a*a + b*a - b*a - b*b
= a*a - b*b

In your first problem a=squareroot(x) and b=squareroot(y), so the answer is x-y.
In your second problem, a=5 and b=squareroot(x), so the answer is 25-x.

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mickey333

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11 years ago

Find the product means to multiply. Use the FOIL method to multiply the the terms in the order of first, outside, inside, and last.

Answers:

1. x-y
2. 25-x

Factor out the common factor: When we factor a polynomial, we are usually only interested in breaking it down into polynomials that have integer coefficients and constants. You can factor using the distributive law: ab+ac = a(b+c)

Answers:

1. 3(x+2)
2. (x+2)(3x-4)
3. 2x (x-3)

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