Multiply the binomials.(3m+4n)(3m−4n)(3m+4n)(3m-4n)

9m2−$$16n29m^2$-16n^29m2$$−16n2

Multiply the binomials. ( 3 m + 4 n ) ( 3 m − 4 n ) (3m+4n)(3m-4n)

Sometimes when you're multiplying binomials in which you have the sum and difference of the same two terms, you can actually have both of the terms that include variables. So, let's take a look at this next practice problem. Fortunately, we actually just treat this the exact same way that we treated every other type of problem like this. The format is still a plus b, a minus b, and so we know that this is going to eventually lead to a difference of squares. That is the result. It's still going to hold true even for these. We still just have to set our a and b and then follow the formula. Alright, so let's take a look at this problem here. We've got three ms plus four n, three ms minus four n. So, it's the same two terms. I've got a, which is my three ms, and then I've got my b, which is the four n. And the only thing that's different about them is that I have an a plus b times an a minus b. So, in other words, I know the result is going to be a squared minus b squared. What I like to do here is I like to sort of make a little table here where I like to figure out what a is. A is three ms. If a is three ms, then what's a squared? Well, a squared is just going to be three m, that whole entire expression, squared. Now, this is where students make a lot of mistakes. They'll say that three m squared is just three m squared because they forget to distribute the exponent to the coefficient as well. You have to distribute the coefficient or sorry the exponent to the coefficient and also the variable. All right, so what happens here is this becomes nine ms squared, and that's what a squared ends up being. All right, so your final answer over here is going to be nine ms squared, and then we still have to figure out the b squared. So, let's actually do the same exact thing over here. If b is equal to four n, then what is b squared? We do the exact same thing we just did to a squared, right? We're going to take this four n and we're going to have to square it. You take the exponent and distribute it to the coefficient and also the variable, so distribute it to the four and also the n and then you end up with not four n squared but 16 n squared, right? That's what b squared ends up becoming And so, therefore, you're just going to plug that into your final answer. You're going to have nine m squared minus 16 n squared. So, here again, it follows the form a squared minus b squared. This is your difference of squares, and this is the final answer. So, let me know if you have any questions, folks. Thanks for watching. I'll see you in the next one.

Multiply the binomials.(3m+4n)(3m−4n)(3m+4n)(3m-4n)

9m2−$$16n29m^2$-16n^29m2$$−16n2

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1. Review of Real Numbers2h 24m

Simplifying Fractions
30m

Evaluating Exponents
14m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 42m

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47m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

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37m

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21m

Percent Problem Solving
1h 4m

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43m

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44m

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24m

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23m

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44m

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38m

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22m

Linear Inequalities in Two Variables
28m

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40m

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41m

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45m

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23m

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10m

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13m

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18m

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18m

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6m

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21m

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20m

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34m

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37m

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11m

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37m

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33m

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35m

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39m

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25m

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24m

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32m

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44m

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27m

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11m

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19m

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23m

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17m

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24m

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29m

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18m

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51m

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Beginning Algebra

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Multiple Choice

Multiply the binomials.
$(3 m + 4 n) (3 m - 4 n)$

$3 n squared minus 4 n squared$

$9 m^{2} + 24 m n - 16 n^{2}$

$9 m^{2} - 24 m n - 16 n^{2}$

$9m^2-16n^2$

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Verified step by step guidance

Recognize that the expression is a product of two binomials: $(3m + 4n)(3m - 4n)$.

Apply the distributive property (also known as FOIL) to multiply each term in the first binomial by each term in the second binomial: multiply \$3m$ by $3m$, $3m$ by $-4n$, $4n$ by $3m$, and $4n$ by $-4n$.

Write out the products explicitly: $3m \times 3m$, $3m \times (-4n)$, $4n \times 3m$, and $4n \times (-4n)$.

Simplify each product: $3m \times 3m = 9m^2$, $3m \times (-4n) = -12mn$, $4n \times 3m = 12mn$, and $4n \times (-4n) = -16n^2$.

Combine like terms: notice that $-12mn$ and \$12mn$ cancel each other out, leaving you with $9m^2 - 16n^2$.

4:15m

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