(x^2+2x+1)(x^2-2x+1)
can someone teach me step by step on this?
do i foil the whole thing?
Are you supposed to expand it or factor it?
It factors into (x+1)^2(x-1)^2
That can also be written
[(x+1)(x-1)]^2 = (x^2-1)^2
which can be multiplied out right way (with FOIL) to give
x^4 -2x^2 +1
You can get the same answer by multiplying (x^2+2x+1) by each of the terms in
x^2 -2x +1
and adding up the results. Many terms would have canceled.
im supposed to expand it
I did, using a shortcut, and gave you the answer.
thank you :)
To multiply the given expression (x^2+2x+1)(x^2-2x+1), you can use the distributive property multiple times or apply the FOIL method. The FOIL method is a popular technique for multiplying two binomials. Let's use the FOIL method to multiply these two expressions step by step:
Step 1: Multiply the first terms of each binomial.
(x^2)*(x^2) = x^4
Step 2: Multiply the outer terms of each binomial.
(x^2)*(-2x) = -2x^3
Step 3: Multiply the inner terms of each binomial.
(2x)*(x^2) = 2x^3
Step 4: Multiply the last terms of each binomial.
(2x)*(-2x) = -4x^2
Step 5: Combine the results from steps 1-4.
x^4 + (-2x^3) + (2x^3) + (-4x^2) = x^4 - 4x^2
Step 6: Multiply the last terms of each binomial.
(2x)*(1) = 2x
Step 7: Add the remaining terms.
x^4 - 4x^2 + 2x + 1
So, the product of (x^2+2x+1)(x^2-2x+1) is x^4 - 4x^2 + 2x + 1.
Using the FOIL method is a helpful way to multiply binomials, especially when dealing with more complex expressions.