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
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
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
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.