Multiply the polynomials using FOIL. ( x 2 − 3 x ) ( 2 x + 8 ) \left(x^2-3x\right)\left(2x+8\right)

Everyone, let's take a look at another practice problem here. We have these 2 polynomials, x squared minus 3x and 2x plus 8, and we're gonna multiply them using foil. Now one of the things that we haven't seen yet is we haven't seen expressions that contain, you know, x squared and binomials and stuff like that, but it actually just works just the same. It doesn't really matter what these terms are. You can always just foil 2 expressions. So let's go ahead and do this. The first and the first terms will be the x squared and the 2 x. So what does that become? Well, usually, the first term ended up being x squared, but we already have an x squared term over here. So x squared times two x will actually become 2 times x cubed. Alright? So you multiply the 2 and another factor of x into the x squared and then you get 2x cubed. Alright? So just be really careful with that. Now we just do the outer terms. So here we have an x squared and an 8. So this becomes 8x squared. So usually the middle two terms would become x, but because we have this first term here that's x squared, you have to do x squared. Alright? So just always, you know, pay attention to the the kind of terms that you have here because some of them might might have already have exponents. Alright. Let's take a look at the next two terms. Here we have negative 3x, right? We always use the sign before times the 2x over here. So if I have negative 3 times 2x, that actually just becomes negative oops, negative 6x2. And then finally what happens is you do the last terms, so this is gonna be negative 3x times 8. Negative 3x times 8 would become negative 24x. Now we just simplify and then we're done. So this just becomes 2x cubed over here, then what I can do is I can combine these 2 like terms. I have the 8x2 and the negative 6x2, and 8 minus 6 just becomes 2. So I have 2x squared, and then I have minus 24x. Alright. So I can't combine any more like terms. So that's my expression. So that is all there is to it. Thanks for watching. Hopefully, you got the right answer. Let's move on.

Multiply the polynomials using FOIL. ( x 2 − 3 x ) ( 2 x + 8 ) \left(x^2-3x\right)\left(2x+8\right)

2 x 3 + 2 x 2 − 6 x − 24 2x^3+2x^2-6x-24

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

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Multiple Choice

Multiply the polynomials using FOIL.
$(x^{2} - 3 x) (2 x + 8)$

$2 x^{2} + 2 x - 24$

$2 x^{3} + 2 x^{2} - 6 x - 24$

$2 x^{3} - 2 x^{2} - 24 x$

$2 x^{3} + 2 x^{2} - 24 x$

Verified step by step guidance

Identify the two binomials to multiply: $\left(x^2 - 3x\right)$ and $\left(2x + 8\right)$.

Apply the distributive property (FOIL method) by multiplying each term in the first binomial by each term in the second binomial: multiply $x^2$ by \$2x$ and $8$, then multiply $-3x$ by $2x$ and $8$.

Write out each product explicitly: $x^2 \times 2x$, $x^2 \times 8$, $-3x \times 2x$, and $-3x \times 8$.

Simplify each product by combining coefficients and adding exponents where applicable: for example, $x^2 \times 2x = 2x^{3}$.

Combine all the simplified terms into a single expression and then combine like terms to write the final polynomial in standard form.

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Multiply the polynomials using FOIL.(x2−3x)(2x+8)\left(x^2-3x\right)\left(2x+8\right)

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Multiply the polynomials using FOIL.
$(x^{2} - 3 x) (2 x + 8)$