Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Consider the functions given below.
P(z)
3z²-1
Q(z)
Match each expression with its simplified form.
3(3-1)
-3x+2
-2(12z-5)
(3z-1)(-3z +2)
-3x + 2
3(3x - 1)
12
(32-1)(-3x + 2)
P(x) = Q(x)
P(x) Q(x)
2(62-1)
(3x - 1)(-3x + 2)
2(12z+1)
(3x - 1)(-3z + 2)

Answer 1

Here are the correct pairings:

`\(P(z) = 3z^2 - 1\) with \(2(3z - 1)\)`

`\(Q(z) = -3z + 2\) with \((3z - 1)(-3z + 2)\)`

`\(P(x) = Q(x)\) with \((3x - 1)(-3x + 2)\)`

`\(3(3-1)\) with \(12\)`

`\(-3x + 2\) with \(-2(3z - 1)\)`

The given functions are
`\(P(z) = 3z^2 - 1\) and \(Q(z) = -3z + 2\)`. To match expressions with their simplified forms, we can evaluate each expression and compare it with the provided functions.

The expression
`\(3(3-1)\)` simplifies to
`\(2 * 3 = 6\), matching with \(2(3z - 1)\).`

The expression
`\(-3x + 2\)` corresponds to
`\(Q(z)\)` as given by
`\(-3z + 2\).`

The expression
`\(12\)` matches with
`\(2(6^2 - 1)\)` after simplification.

The expression
`\((3z - 1)(-3z + 2)\)` corresponds to
`\(P(z)\)`as given by
`\(3z^2 - 1\).`

Finally, the expression
`\((3x - 1)(-3x + 2)\)` represents
`\(P(x) = Q(x)\),` indicating that
`\(P(x)\) and \(Q(x)\)` are equal.

In summary, the correct pairings are:
`\(2(3z - 1)\) with \(3(3-1)\), \(-3z + 2\) with \(-3x + 2\), \(12\) with \(2(6^2 - 1)\), and \((3z - 1)(-3z + 2)\) with \(P(z)\), and \((3x - 1)(-3x + 2)\) with \(P(x) = Q(x)\).`