2x-3 parenthesis 2x plus 3 parenthesis equals?

Answer 1

(2x-3)(2x+3) can be multiplied out using the FOIL method, which stands for:

First

Outer

Inner

Last

This method only works for the multiplication of two binomials, so don't rely exclusively upon it.

For the "first" part, multiply the two first terms of the binomials together:

(2x)(2x)=4x2

For the "outer" part, multiply the two outermost terms together:

(2x)(3)=6x

For the "inner" part, mulitply the two innermost terms together:

(2x)(-3)=-6x

For the "last" part, mulitply the two last terms of each binomial together:

(3)(-3)=-9

Add all of these sub-calculations together to get your final result:

4x2+6x-6x-9

As you can see, 6x-6x=0, so these two terms will cancel out, leaving:

4x2-9

Another way of doing this multiplication is to see it as an application of the distributive property, but instead of a single number distributed across a binomial, it is another binomial. This is what the FOIL method essentially does, but it creates a handy mnemonic to remember it. To see it as a distributive problem, visualize it like this as I distribute (2x-3) across (2x+3):

(2x-3)(2x+3)=(2x-3)(2x)+(2x-3)(3)=(4x2-6x)+(6x-9)=4x2-9

As you can see, the same answer is reached. This method of distributing one entire term across the other polynomial holds true for more complicated multiplications, so it is the most accurate way to memorize how to handle these problems. A simplification of something like this:

(x-7)(5x4+4x3-x2+9x-2)

cannot be handled with such a convenient crutch as the FOIL method, but realizing it is simply distribution makes it very doable:

(x-7)(5x4)+(x-7)(4x3)-(x-7)(x2)+(x-7)(9x)-(x-7)(2)

(5x5-35x4)+(4x4-28x3)-(x3-7x2)+(9x2-63x)-(2x-14)

5x5-35x4+4x4-28x3-x3+7x2+9x2-63x-2x+14

5x5-31x4-29x3+16x2-65x+14

And in case that side-track example distracted you from the real answer, it was 4x2-9