Expand and simplify four brackets
three 𝑧 plus five minus four brackets 𝑧 minus one.
It’s really important that we’re
very careful with this question. A common mistake is to spot the two
brackets and think that we need to apply the FOIL method for expanding brackets. However, the two brackets in this
question are not multiplying each other. They have their own constants. Instead, we’re going to multiply
each bracket individually, watching carefully for the signs in the second part of
Remember when expanding a bracket,
we need to make sure that the number on the outside multiplies by everything on the
inside of that bracket. Four multiplied by three is 12. So four multiplied by three 𝑧 is
12𝑧. Four multiplied by five is 20. The first part of our expression is
12𝑧 plus 20.
Now, the elements in the second
bracket are all being multiplied by negative four. Negative four multiplied by 𝑧 is
negative four 𝑧 and negative four multiplied by negative one is positive four. The second part of our expression
then is negative four 𝑧 plus four. Finally, we mustn’t forget to
simplify our expression by collecting like terms. 12𝑧 minus four 𝑧 is eight 𝑧 and
20 plus four is 24. Our expression simplifies to eight
𝑧 plus 24.
Simplify four 𝑥 cubed 𝑦 squared
multiplied by eight 𝑥 to the power of four multiplied by 𝑦.
Here, we have two terms that are
being multiplied. Let’s start by multiplying the
numbers. Four multiplied by eight is 32. Next, we can multiply the 𝑥s. Remember when we’re multiplying two
expressions with indices, as long as the base which is in this case the large letter
is the same, we can add the powers. So 𝑥 to the power of 𝑎 multiplied
by 𝑥 to the power of 𝑏 would be 𝑥 to the power of 𝑎 plus 𝑏. In this case, 𝑥 cubed multiplied
by 𝑥 to the power of four is 𝑥 to the power of seven.
Finally, let’s multiply the
𝑦s. When we have 𝑦 all by itself, its
power though it’s not written explicitly is one. 𝑦 squared multiplied by 𝑦 to the
power of one is 𝑦 cubed since once again we add the powers. Popping all this together, we get
our answer to be 32𝑥 to the power of seven 𝑦 cubed.