Year 8 Mathematics worksheet matching factorized expressions to their expanded forms.

To solve this problem, we need to expand each of the factorized expressions and match them with their corresponding expanded forms. Let's go through each factorized expression step by step.

Factorized Expression 1: \( 6x(4x^2 + 2x + 3) \)

- Expand:
\[
6x \cdot 4x^2 + 6x \cdot 2x + 6x \cdot 3 = 24x^3 + 12x^2 + 18x
\]
- Match: None of the given expanded forms match this result.

Factorized Expression 2: \( 7pqr(5q - 4p - 7r) \)

- Expand:
\[
7pqr \cdot 5q + 7pqr \cdot (-4p) + 7pqr \cdot (-7r) = 35pq^2r - 28p^2qr - 49pqr^2
\]
- Match: Expanded form 10.

Factorized Expression 3: \( 3t^3(25 + 11t) \)

- Expand:
\[
3t^3 \cdot 25 + 3t^3 \cdot 11t = 75t^3 + 33t^4
\]
- Match: Expanded form 4 (after correcting the typo in the expanded form to \( 75t^3 + 33t^4 \)).

Factorized Expression 4: \( -12x(3a - 4b) \)

- Expand:
\[
-12x \cdot 3a + (-12x) \cdot (-4b) = -36ax + 48bx
\]
- Match: Expanded form 3.

Factorized Expression 5: \( 15xy(3x + 2 + 4y) \)

- Expand:
\[
15xy \cdot 3x + 15xy \cdot 2 + 15xy \cdot 4y = 45x^2y + 30xy + 60xy^2
\]
- Match: Expanded form 11.

Factorized Expression 6: \( 30ax(7 - 2b - 3dx^2) \)

- Expand:
\[
30ax \cdot 7 + 30ax \cdot (-2b) + 30ax \cdot (-3dx^2) = 210ax - 60abx - 90adx^3
\]
- Match: Expanded form 5.

Factorized Expression 7: \( 6(5x^2 + 3y - 7y^2) \)

- Expand:
\[
6 \cdot 5x^2 + 6 \cdot 3y + 6 \cdot (-7y^2) = 30x^2 + 18y - 42y^2
\]
- Match: Expanded form 1.

Factorized Expression 8: \( -8xy(2xy + 3y + 2x) \)

- Expand:
\[
-8xy \cdot 2xy + (-8xy) \cdot 3y + (-8xy) \cdot 2x = -16x^2y^2 - 24xy^2 - 16x^2y
\]
- Match: Expanded form 12.

Factorized Expression 9: \( -23o^2(2o + 3) \)

- Expand:
\[
-23o^2 \cdot 2o + (-23o^2) \cdot 3 = -46o^3 - 69o^2
\]
- Match: Expanded form 8.

Factorized Expression 10: \( 6x(10 - 2x^2 + 11ax^3) \)

- Expand:
\[
6x \cdot 10 + 6x \cdot (-2x^2) + 6x \cdot 11ax^3 = 60x - 12x^3 + 66ax^4
\]
- Match: Expanded form 7.

Factorized Expression 11: \( 45(x^2 + 2) \)

- Expand:
\[
45 \cdot x^2 + 45 \cdot 2 = 45x^2 + 90
\]
- Match: Expanded form 6.

Factorized Expression 12: \( 6bd^2(a^2 - 11) \)

- Expand:
\[
6bd^2 \cdot a^2 + 6bd^2 \cdot (-11) = 6a^2bd^2 - 66bd^2
\]
- Match: Expanded form 2.

Final Matches:

1. \( 6x(4x^2 + 2x + 3) \) → No match (error in problem setup)
2. \( 7pqr(5q - 4p - 7r) \) → 10
3. \( 3t^3(25 + 11t) \) → 4
4. \( -12x(3a - 4b) \) → 3
5. \( 15xy(3x + 2 + 4y) \) → 11
6. \( 30ax(7 - 2b - 3dx^2) \) → 5
7. \( 6(5x^2 + 3y - 7y^2) \) → 1
8. \( -8xy(2xy + 3y + 2x) \) → 12
9. \( -23o^2(2o + 3) \) → 8
10. \( 6x(10 - 2x^2 + 11ax^3) \) → 7
11. \( 45(x^2 + 2) \) → 6
12. \( 6bd^2(a^2 - 11) \) → 2

Boxed Answer:

\[
\boxed{
\begin{array}{ll}
1 & \text{No match} \\
2 & 10 \\
3 & 4 \\
4 & 3 \\
5 & 11 \\
6 & 5 \\
7 & 1 \\
8 & 12 \\
9 & 8 \\
10 & 7 \\
11 & 6 \\
12 & 2 \\
\end{array}
}
\]