Video: Expanding Complicated Single Bracket Expressions

Expand and simplify 4(2𝑥 + 3) + 2(4𝑥 + 4).

02:28

Video Transcript

Expand and simplify four multiplied by two 𝑥 plus three plus two multiplied by four 𝑥 plus four.

To solve this problem, first of all, we’re actually going to expand our parentheses. And the way we do this is by multiplying the number that’s outside that parentheses by each of the terms within. So we’re gonna start with the first parenthesis and we’re gonna multiply our four by first term, which is our two 𝑥, which gives us eight 𝑥. And next, we’re gonna multiply our four by our second term, which is positive three, which gives us positive 12.

And now, we can move on to the second parenthesis. And we’re gonna start by multiplying our two, which is outside the parenthesis, by our first term, which is four 𝑥. And this is gonna give us an answer of positive eight 𝑥.

This brings us to a little tip. And the tip is well be careful with the signs when expanding. In our question, it’s positive two. So it’s not a problem. It’s just blind multiplying two by each of the terms within.

However, if it was negative, this can actually cause some challenges. For example, if I had negative two outside the parenthesis and negative four 𝑥 plus four within the parenthesis, I will get eight 𝑥 minus eight and I get eight 𝑥 because we have negative two multiplied by negative four 𝑥. So negative multiplied by negative gives us positive. And then I have negative eight because we got negative two multiplied by positive four. So that’s going to give us negative, so negative eight. So this is something to be careful of when you do in this kind of problem.

So we can now get back to the question. And actually, what we can see is we want to multiply our positive two by the second term in the second parenthesis. So it’s gonna be two multiplied by four, which is gonna give us eight. So we now got eight 𝑥 plus 12 plus eight 𝑥 plus eight.

So we can now move on to the second part of our question, which is simplify. So we’re now gonna simplify by collecting like terms. So first of all, we have eight 𝑥 plus eight 𝑥, which is gonna give us 16𝑥. As you noticed, I’ve actually underlined the sign in front of the second eight 𝑥. That’s just to make sure.

And in this case, yes, it’s positive eight 𝑥. And then, we have positive 12 add eight, which is gonna give us positive 20. So therefore, we can say expanded and simplified, our expression is equal to 16𝑥 plus 20.

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