I need to find the equivalent to (2x-3)^2
I need to find the equivalent to (2x-3)^2
Hi Erika,
Let's begin by writing out the expression we need to simplify: (2x - 3)^2
First, we know that squaring an expression is the equivalent of multiplying the expression by itself.
So we can rewrite our exprssion as: (2x - 3)(2x - 3)
Now we can use FOIL to multiply these two binomials.
FOIL is an acronym which stands for <F>irst, <O>utside, <I>nside, and <L>ast.
So let's apply FOIL to our binomial multiplication: (2x - 3)(2x -3)
Multiplying the <F>irst terms of each binomial: (2x)(2x) = 4x^2
Multiplying the <O>utside terms of each binomial: (2x)(-3) = -6x
Multiplying the <I>nside terms of each binomial: (-3)(2x) = -6x
Multiplying the <L>ast terms of each binomial: (-3)(-3) = 9
Now let's collect all the terms of our multiplication results: 4x^2 - 6x - 6x + 9
Finally, we'll combine like terms (our x terms) for our final result: 4x^ -12x + 9
Thanks for submitting your question.
Regards, Jordan.
You can use (a+b)^{2} = a^{2}+2ab+b^{2}.
(2x - 3)^{2} = (2x)^{2} + 2(2x)(-3) + (-3)^{2} = 4x^{2} - 12x + 9
Or you can use FOIL.
(2x - 3)^{2} = (2x - 3)(2x - 3) = (2x)^{2} + (2x)(-3) + (-3)(2x) + (-3)^{2} = 4x^{2} - 12x + 9
First Outer Inner Last
(a + b)^{2} = (a + b)(a + b) = a^{2} + ab + ba + b2 = a^{2} + 2ab + b^{2}.
Above I've given a short derivation of a very useful formula which demonstrates how to "square a binomial," which is just a fancy way of saying "raise the sum to the 2nd power."
In short, write the squared term as the term multiplied by itself. Then apply FOIL: First, Outer, Inner, Last. In the case of "squaring a binomial," the Outer and Inner terms are equal [ab = ba], and they can be added to give 2ab.
I hesitate to simply work out the example you give (I will leave that to you, or the less hesitant tutors here.) So instead, here's an example that's similar, and demonstrates the technique just as well.
(5x - 2)^{2} = (5x - 2)(5x - 2) = (5x)^{2} -10x -10x + (-2)^{2 }= 25x^{2} - 20x + 4.
Now try your problem.
I hope this helped. If not, I or another tutor will be happy to assist you further until you've got the hang of these.
Do you want to expand it?
Here you go.
(2x-3)^2 = (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9
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Attn: (a+b)^2 = a^2 + 2ab + b^2