# (a+b)^2 using mulitplying in brackets

1. Feb 2, 2012

### morbello

question im working on at the moment is squares

when is (a+b)^2 eather (a+b)(a+b) useing foils law or when (a+b)(a-b) using foils law.
im stuck to when you use which one.

i think they are when you use quadratic x^2+x+1=0 for the first one or -1 at the end for the second one.
i hope you can help.

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3. The attempt at a solution
1. The problem statement, all variables and given/known data

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3. The attempt at a solution

2. Feb 2, 2012

### eumyang

When you square a number, you multiply that number by itself. So
(a + b)2 = (a + b)(a + b). Also,
(a - b)2 = (a - b)(a - b).

Well, you won't be able to use any of the special product patterns with either of the quadratics above.
(a + b)2 = a2 + 2ab + b2, and
(a - b)2 = a2 - 2ab + b2, and
they don't fit in either quadratic above.

3. Feb 2, 2012

### morbello

thank you,it would only be just with a quadratic and factoring you have + and a - would this be using the which (a+b)^2 or is this some thing else.

4. Feb 2, 2012

### eumyang

4x2 + 20x + 25 = 0,
you can use the special product
(a + b)2 = a2 + 2ab + b2
because
4x2 + 20x + 25 = (2x)2 + 2(2x)(5) + 52,
and this follows the pattern
a2 + 2ab + b2.

So
4x2 + 20x + 25 = 0
(2x)2 + 2(2x)(5) + 52 = 0
(2x + 5)2 = 0
... and so on.

x2 - 14x + 49 = 0,
you can use the special product
(a - b)2 = a2 - 2ab + b2
because
x2 - 14x + 49 = x2 - 2(x)(7) + 72,
which follows the pattern
a2 - 2ab + b2.

So
x2 - 14x + 49 = 0
x2 - 2(x)(7) + 72 = 0
(x - 7)2 = 0.
... etc.

You mentioned the sum and difference pattern, which is
(a + b)(a - b) = a2 - b2.

You can use this pattern in a quadratic like this one:
25x2 - 64 = 0,
like this:
25x2 - 64 = 0
(5x)2 - 82 = 0
(5x + 8)(5x - 8) = 0
... etc.

This is an example of a quadratic that would not fit any of the three patterns above:
x2 + 12x - 64 = 0
However, it can be factored into
x2 + 12x - 64 = 0
(x + 16)(x - 4) = 0
... and can be solved by using the zero product property.

5. Feb 2, 2012

### morbello

Thank you ,this is helpfull.Have a good day.may your pc never lag :)