Multiply the binomials. ( x 2 − 1 ) ( x 2 + 1 ) (x^2-1)(x^2+1)

If you haven't already, go ahead and pause the video and see if you can try this one out on your own. Here we've got these two binomials x squared minus one, x squared plus one. I notice that they're in the form where I have an a and a b. I've got the same two terms and the only difference between them is that we have a minus sign and a plus sign but they're multiplied together. Now, just because the minus sign comes first doesn't mean that we do anything differently. This is still of the form a plus b times a minus b. The fact that the a minus b comes first doesn't really mean anything because we still multiply this together. The end result is still going to be a squared minus b squared, the difference of squares. So all you have to do is just figure out what is our a and a squared and then b and b squared. So, our a in this situation is actually already something that is squared. Our a is x squared. Now, again, if this is our a and this is x squared, then what does a squared end up becoming? Well, it's just the first term, we have the x squared, and you would just have to square that. So, sometimes we can see that our a term in our format here is already a term that is squared, but we don't really treat it any differently. We're still going to have to square that. So, what we have is x squared squared, in which we have a power to a power. In this case, this should becomes x to the fourth. Alright? So, we really just don't handle this any differently here. It's just that in some cases, you might have to square something that is already to another power. Okay? So, now we're going to go ahead and do the same exact thing for b, except our b is a little bit more straightforward because this is just a number or a constant, things we've already seen before. So, what do we do with one? Well, if one is b, b squared is also just going to be one. It doesn't really change because one squared is still just one. So, in other words, our final result here is going to be a squared, which is going to be x to the fourth, minus b squared, which is just the one. Alright? Again, if you ever sort of are doubting this, you can always just sort of use the foil method to multiply this out. You'll always notice that the middle terms will cancel and leaving you with x to the fourth minus one. That's your final answer. Let me know if you have any questions and I'll see you in the next one.

6. Exponents, Polynomials, and Polynomial Functions

Special Products

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Special Products

Struggling with Intermediate Algebra?

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Multiple Choice

Multiply the binomials.
$(x^{2} - 1) (x^{2} + 1)$

$x squared minus 1$

$x^{4} + 2 x^{2} - 1$

$x^{4} - 2 x^{2} + 1$

$x^4-1$

Verified step by step guidance

Identify the binomials to multiply: $(x^2 - 1)$ and $(x^2 + 1)$.

Apply the distributive property (also known as FOIL for binomials) to multiply each term in the first binomial by each term in the second binomial: multiply $x^2$ by $x^2$, then $x^2$ by \$1$, then $-1$ by $x^2$, and finally $-1$ by $1$.

Write out the products explicitly: $x^2 \times x^2$, $x^2 \times 1$, $-1 \times x^2$, and $-1 \times 1$.

Simplify each product: $x^2 \times x^2 = x^{4}$, $x^2 \times 1 = x^{2}$, $-1 \times x^2 = -x^{2}$, and $-1 \times 1 = -1$.

Combine like terms: $x^{4} + x^{2} - x^{2} - 1$, then simplify by canceling $x^{2}$ and $-x^{2}$ to get the final expression.

5:43m

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Master Squaring Binomials with a bite sized video explanation from Patrick Ford

Struggling with Intermediate Algebra?

Multiply the binomials.(x2−1)(x2+1)(x^2-1)(x^2+1)

Watch next

Multiply the binomials.
$(x^{2} - 1) (x^{2} + 1)$