(a+b)^2 using mulitplying in brackets

[morbello]

question I am 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.

Homework Equations

The Attempt at a Solution

 

[eumyang]

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.

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).

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.

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.

 

[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.

 

[eumyang]

For example, if you had a quadratic
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.

Another example: for this quadratic,
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.

 

[morbello]

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