Perform the indicated operation.(x3+3x2−7x)+2(x3−5x2+9x+4)\left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right)(x3+3x2−7x)+2(x3−5x2+9x+4)

3 x 3 − 7 x 2 + 11 x + 8 3x^3-7x^2+11x+8 3 x 3 − 7 x 2 + 11 x + 8

Perform the indicated operation. ( x 3 + 3 x 2 − 7 x ) + 2 ( x 3 − 5 x 2 + 9 x + 4 ) \left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right) ( x 3 + 3 x 2 − 7 x ) + 2 ( x 3 − 5 x 2 + 9 x + 4 )

Welcome back, everyone. So here we have some expressions. I got this polynomial over here, and I've got this other polynomial, and I wanna add them together. So I'm just gonna go ahead and add everything, and then I'm gonna have to go and start working on the combining the like terms. The one thing I have though is I have a 2 that's outside of this expression, so I actually have to do something first. So I'm gonna rewrite this x cubed over here plus 3x squared minus 7x. So nothing about that changed, But now what I have to do is I have to distribute the 2 into everything that is inside that parenthesis. So the 2 goes into the x cubed, the 5x squared, the 9, and the 4. So then what happens here is this 2x cubed just becomes 2x cubed, then I have 2 times negative 5x squared, this becomes negative 10x squared, this 9x over here becomes 18x, and then this 2 times 4 just becomes 8. So now what happens is now that I've distributed that 2 inside of everything in the parentheses, now I can basically drop the parentheses from that expression, and now I can get started on combining like terms. Okay? So what are my like terms over here? So I've got an x cubed and a 2 x cubed. And remember, you wanna keep the sign, always keep the signs attached to them. Are there any other x cubes? No. What about x squared? I've got a 3 x squared that's positive. I've got a negative 10x squared that's negative. And that's it. There's no more x squared. What about x's? I've got 1 7x over here. It's negative, and I've got nothing else. Oh, actually, sorry. There was a there's another x over here. Oops. Sorry about that. And there's another 18x. So that's 18x. And then finally, what happens is there's just one constant that's out by itself, and that's just gonna be the, the plus 8. Okay? So here's what happens. I'm gonna group together and combine the like terms. This is 3x cubed. Then what happens is I've got the 3x squared and the negative 10x squared that combines down to form, negative 7x squared. Right? 3 minus 10. Now what happens is I gotta combine the negative 7 and the 18. So 18 minus 7, so that just becomes let's see. 18 minus 7, that becomes plus 11 x. And then finally, I just have the plus 8 over here, and that just drops down to plus 8. Alright. So that is my algebraic expressions, my polynomial. Sorry. And I can't simplify this any further. All the like terms have been combined. So hopefully that made sense. Hopefully, you got it right. I'll see you in the next video.

Perform the indicated operation. ( x 3 + 3 x 2 − 7 x ) + 2 ( x 3 − 5 x 2 + 9 x + 4 ) \left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right) ( x 3 + 3 x 2 − 7 x ) + 2 ( x 3 − 5 x 2 + 9 x + 4 )

3 x 3 − 7 x 2 + 11 x + 8 3x^3-7x^2+11x+8 3 x 3 − 7 x 2 + 11 x + 8

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

2 x 3 − 2 x 2 + 2 x + 4 2x^3-2x^2+2x+4 2 x 3 − 2 x 2 + 2 x + 4

3 x 3 − 2 x 2 + 2 x + 4 3x^3-2x^2+2x+4 3 x 3 − 2 x 2 + 2 x + 4

0. Review of Algebra

Polynomials Intro

College Algebra

0. Review of Algebra

Polynomials Intro

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Multiple Choice

Perform the indicated operation.
$\left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right)$

$2x^3-2x^2+2x+6$

$3x^3-7x^2+11x+8$

$2x^3-2x^2+2x+4$

$3x^3-2x^2+2x+4$

Verified step by step guidance

First, distribute the 2 across the polynomial (x^3 - 5x^2 + 9x + 4). This means you will multiply each term inside the parentheses by 2.

After distributing, you will have: 2(x^3) + 2(-5x^2) + 2(9x) + 2(4), which simplifies to 2x^3 - 10x^2 + 18x + 8.

Now, add the result from the distribution to the original polynomial (x^3 + 3x^2 - 7x).

Combine like terms: Add the coefficients of x^3, x^2, x, and the constant terms separately.

The final expression after combining like terms will be the simplified polynomial.

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