Multiply the binomials.(y+18)(y−18)\left(y+\frac18\right)\left(y-\frac18\right)

y 2 − 1 64 y^2-\frac{1}{64} y 2 − 64 1

Multiply the binomials. ( y + 1 8 ) ( y − 1 8 ) \left(y+\frac18\right)\left(y-\frac18\right)

In some of your multiplication problems involving the sum and difference of the same two terms, you may run across some terms that have fractions in them, and that's perfectly fine. So, let's kick off our practice set by looking at this example here. We got y plus one eighth times y minus one eighth. As a reminder, whenever you run across a multiplication of two binomials of this form, a plus b times a minus b, the result is always a squared minus b squared, so we just have to determine what's a and what's b and then just follow the formula. So, we have this expression y plus one eighth y minus one eighth. So, in other words, I see the same two terms y and then the other same two terms one eighth over here. The only thing that's different is that we have one with a plus sign and then one with a minus sign, but we're multiplying. So, really what happens is we just have to figure out what's our a. Our a in this case is surely just y, so therefore our a squared is just going to be y squared. So, that means our result is just going to be y squared and then minus and then we're going to have b squared. So, what is b squared? Well, to figure that out we're just going to take a look at what b is. B in this case is one eighth. So, when we do one eighth squared, what does that become? Well, this is really just one over eight that gets squared. We've seen this before. You just basically square, both sides, the top and the bottom. So, one squared is just one and eight squared is 64 on the bottom. So, this is just going to be y squared minus one over sixty fourth, and we again we can see this is of the form a squared minus b squared over here. Alright, so that's really all there is to it. This is the final answer. Let me know if you have any questions and let's keep going.

Multiply the binomials. ( y + 1 8 ) ( y − 1 8 ) \left(y+\frac18\right)\left(y-\frac18\right)

y 2 − 1 64 y^2-\frac{1}{64} y 2 − 64 1

y 2 − 1 4 y − 1 64 y^2-\frac14y-\frac{1}{64}

y 2 + 1 4 y − 1 64 y^2+\frac14y-\frac{1}{64}

y 2 + 1 64 y^2+\frac{1}{64} y 2 + 64 1

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.
$(y + \frac{1}{8}) (y - \frac{1}{8})$

$y^{2} - \frac{1}{4} y - \frac{1}{64}$

$y^{2} + \frac{1}{4} y - \frac{1}{64}$

$y^2-$\frac{1}{64}$$

$y^2+$\frac{1}{64}$$

Verified step by step guidance

Recognize that the expression $ \left(y+\frac{1}{8}\right)\left(y-\frac{1}{8}\right) $ is a product of two binomials in the form $ (a+b)(a-b) $, which is a difference of squares pattern.

Recall the difference of squares formula: $ (a+b)(a-b) = a^2 - b^2 $. Here, $ a = y $ and $ b = \frac{1}{8} $.

Square each term separately: calculate $ a^2 = y^2 $ and $ b^2 = \left(\frac{1}{8}\right)^2 $.

Substitute these squared terms back into the difference of squares formula to get $ y^2 - \left(\frac{1}{8}\right)^2 $.

Simplify the squared fraction $ \left(\frac{1}{8}\right)^2 $ to $ \frac{1}{64} $, resulting in the final expression $ y^2 - \frac{1}{64} $.

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.(y+18)(y−18)\(\left\)(y+\(\frac\)18\(\right\))\(\left\)(y-\(\frac\)18\(\right\))

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Multiply the binomials.
$(y + \frac{1}{8}) (y - \frac{1}{8})$