Video: Pack 3 • Paper 1 • Question 2

Pack 3 • Paper 1 • Question 2

02:11

Video Transcript

Expand and fully simplify 𝑥 plus eight multiplied by 𝑥 minus seven.

So if we’re gonna expand and fully simplify this, what we’re gonna do is actually multiply each of the terms in our first bracket by each of the terms in the second bracket. Okay, so let’s get on and solve the problem.

So what I wanna do is I wanna actually start by multiplying the first term in each of our brackets. So that case I’m gonna multiply 𝑥 by 𝑥 and this is equal to 𝑥 squared because 𝑥 multiplied by 𝑥 gives us 𝑥 squared. And what I’ve done is actually drawing a line as well to show that we’ve actually multiplied these terms together.

Okay, so now, what I need to do is actually multiply this 𝑥 term in the first bracket by the second term in the second bracket. So when we do this, we get negative seven 𝑥 because actually having a negative multiplied by a positive gives us negative seven 𝑥.

So the next step is to actually multiply the second term in the first bracket by the first term in the second bracket. So we get positive eight multiplied by 𝑥 which gives us positive eight 𝑥. And then, finally, we’re gonna multiply the last term in the first bracket, so our eight, multiplied by the last term in the second bracket, which is gonna be negative seven. So positive eight multiplied by negative seven gives us negative 56.

So there we go, we’ve actually completed the first part of the question. So we’ve actually expanded our brackets. Now, we move on to the second part. Now, the second part of the question tells us that we need to fully simplify. So let’s do that. Let’s collect like terms.

The most common mistake at this stage is that students try to combine 𝑥 squared and 𝑥 terms, but this can’t happen. You can only combine, add or subtract, 𝑥 terms that are in fact of the same order or the same power.

So therefore, we’re just gonna get one 𝑥 squared, so just 𝑥 squared. And then, we’ve got negative seven 𝑥 plus eight 𝑥. So we’re actually going up from negative seven. So that’s gonna give us positive one 𝑥. So we just write that as plus 𝑥. And then, we’re just left with our minus 56.

So therefore, if we look, we’ve actually done the second part cause we fully simplified as well. So therefore, what we can say is that if we expand and fully simplify 𝑥 plus eight multiplied by 𝑥 minus seven, we get 𝑥 squared plus 𝑥 minus 56.

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