Multiply the polynomials using special product formulas. (5x−9)(5x+9)\left(5x-9\right)\left(5x+9\right)(5x−9)(5x+9)

25 x 2 − 81 25x^2-81 25 x 2 − 81

Multiply the polynomials using special product formulas. ( 5 x − 9 ) ( 5 x + 9 ) \left(5x-9\right)\left(5x+9\right) ( 5 x − 9 ) ( 5 x + 9 )

Everyone. So let's take a look at our practice problem here. So we've got 5x minus 9 multiplied by 5x+9. We're gonna multiply these polynomials by using some of the special product formulas that we saw in the previous video, and I've got them over here just as a reference. So let's take a look. I've basically got the same exact expression 5x and the 9, but the only thing that's different between them is a sign difference. I've got minus 9 over here and then plus 9. Pretty much always whenever this happens whenever you have a sign difference just between two numbers, but everything is the same, it's gonna be this over here. This sort of pattern where you have a plus b and a minus b. So you have this a and b, but the only difference is the sign. And so what your answer is gonna be is it's gonna be the a2b2. Remember, this is called the difference of squares. So really this is just the same thing as a b, a plus b. Now in our formula sheet, we saw plus and minus, but actually you can flip the order of these things and that's perfectly fine to do. Because remember, you know, multiplication doesn't have a specific order. So the answer of this is just gonna be a squared minus b squared. So we're basically done. We know what the answer is gonna look like. Now we just have to figure out what is a, what's b, and then what's a2 and b2. So if you take a look at this expression here, I have 5x minus 9 and then 5x+9. So the a in this case is actually 5x, not just x. It's the whole thing of 5x. And so b over here is a little bit more straightforward because I have minus 9+9, so b is my 9. So what that means here is that if a is equal to 5 x, that means that a squared is equal to 5 x, that whole thing that whole thing squared. So if I square this expression, the the 5 squared becomes 25 and the x becomes x squared. Alright? And if I take the b term over here and square that, that's a little bit more straightforward because this just becomes 81. All I have to do is just pop these expressions into my formula, and I'm done. So this whole thing just becomes 25x2-eighty 1. Alright? And that is your final answer. Okay? So pretty straightforward. Let me know if you have any questions. Thanks for watching.

Multiply the polynomials using special product formulas. ( 5 x − 9 ) ( 5 x + 9 ) \left(5x-9\right)\left(5x+9\right) ( 5 x − 9 ) ( 5 x + 9 )

25 x 2 − 81 25x^2-81 25 x 2 − 81

5 x 2 − 81 5x^2-81 5 x 2 − 81

25 x 2 + 90 x + 81 25x^2+90x+81 25 x 2 + 90 x + 81

25 x 2 − 90 x + 81 25x^2-90x+81 25 x 2 − 90 x + 81

0. Review of Algebra

Multiplying Polynomials

College Algebra

0. Review of Algebra

Multiplying Polynomials

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Multiple Choice

Multiply the polynomials using special product formulas.
$\left(5x-9\right)\left(5x+9\right)$

$5x^2-81$

$25x^2-81$

$25x^2+90x+81$

$25x^2-90x+81$

Verified step by step guidance

Recognize that the expression $(5x - 9)(5x + 9)$ is a product of two binomials in the form $(a - b)(a + b)$, which is a special product known as the difference of squares.

Recall the difference of squares formula: $(a - b)(a + b) = a^2 - b^2$. This formula simplifies the multiplication of binomials into a subtraction of squares.

Identify $a$ and $b$ in the given expression: here, $a = 5x$ and $b = 9$.

Apply the difference of squares formula: substitute $a = 5x$ and $b = 9$ into $a^2 - b^2$ to get $(5x)^2 - 9^2$.

Calculate $(5x)^2$ and $9^2$: $(5x)^2 = 25x^2$ and $9^2 = 81$. Therefore, the expression simplifies to $25x^2 - 81$.

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