Video: AF5P1-Q04-147147517327

Circle the expression that cannot be written as 4𝑧³. [A] 2 βˆ’ 2 βˆ’ 𝑧 βˆ’ 𝑧 βˆ’ 𝑧? [B] (2𝑧)Β³/2? [C] 𝑧³ + 𝑧³ + 𝑧³ + 𝑧³ [D] 2(2𝑧³)

04:52

Video Transcript

Circle the expression that cannot be written as four 𝑧 cubed. Is it two minus two minus 𝑧 minus 𝑧 minus 𝑧? Is it two 𝑧 all cubed divided by two? Is it 𝑧 cubed plus 𝑧 cubed plus 𝑧 cubed plus 𝑧 cubed? Or is it two multiplied by two 𝑧 cubed?

Let’s consider each of the expressions in turn and try and simplify them. One of them will not be equal to four 𝑧 cubed. The first expression said the following, two minus two minus 𝑧 minus 𝑧 minus 𝑧. In order to simplify this expression, we need to group, or collect, the like terms. We need to group the constants and we need to group the 𝑧s. Two minus two is equal to zero. And negative 𝑧 minus 𝑧 minus 𝑧 gives us negative three 𝑧. The expression simplifies to zero minus three 𝑧. This is equal to negative three 𝑧.

As we are looking for the expression that cannot be written as four 𝑧 cubed, this suggests that this is the correct answer. However, it is worth checking the three other options to make sure we haven’t made a mistake with our simplifying.

The second expression said the following, two 𝑧 all cubed divided by two. We could cube two 𝑧 in one of two ways. We could multiply two 𝑧 by two 𝑧 and by two 𝑧 again. Or we could cube each of the terms separately, two cubed multiplied by 𝑧 cubed. Two cubed is the same as two multiplied by two multiplied by two. This is equal to eight. As two multiplied by two equals four and multiplying this by two is eight.

The expression, therefore, simplifies to eight 𝑧 cubed over two, or eight 𝑧 cubed divided by two. We can divide both the numerator and denominator by two. Eight divided by two is equal to four. And two divided by two is equal to one. Four 𝑧 cubed divided by one is the same as four 𝑧 cubed. Therefore, the expression two 𝑧 all cubed divided by two can be written as four 𝑧 cubed. This is not the correct answer.

The third option was 𝑧 cubed plus 𝑧 cubed plus 𝑧 cubed plus 𝑧 cubed. As all four of these terms have the same power, or index, in this case three, we can group, or collect, the like terms. 𝑧 cubed is the same as one 𝑧 cubed. Therefore, adding 𝑧 cubed, 𝑧 cubed, 𝑧 cubed, and 𝑧 cubed gives us four 𝑧 cubed. As with the second option, this expression can be written as four 𝑧 cubed, so it’s not the correct answer.

The final option has a two outside the bracket and two 𝑧 cubed inside it. This means that we are multiplying two by two 𝑧 cubed. Two 𝑧 cubed is the same as two multiplied by 𝑧 cubed. This means that the expression can be rewritten as two multiplied by two multiplied by 𝑧 cubed. As multiplication is commutative, we can multiply the terms in any order.

Let’s first multiply two by two. This gives us four. So, we are left with four multiplied by 𝑧 cubed. This can be written as four 𝑧 cubed. Therefore, two multiplied by two 𝑧 cubed is equal to four 𝑧 cubed. And once again, this is not the correct answer.

The expression that cannot be written as four 𝑧 cubed is the first one, two minus two minus 𝑧 minus 𝑧 minus 𝑧, which instead simplifies to negative three 𝑧. The other three options can all be simplified to four 𝑧 cubed.

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