Algebra Factorizing & Expanding Brackets worksheet - Free Printable

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: This matches with Expanded Form 10.

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

- Expand:
\[
3t^3 \cdot 25 + 3t^3 \cdot 11t = 75t^3 + 33t^4
\]
- Match: This matches with Expanded Form 4.

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

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

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

- Expand:
\[
-23o^2 \cdot 2o + (-23o^2) \cdot 3 = -46o^3 - 69o^2
\]
- Match: This matches with 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: This matches with Expanded Form 7.

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

- Expand:
\[
45 \cdot x^2 + 45 \cdot 2 = 45x^2 + 90
\]
- Match: This matches with 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: This matches with Expanded Form 2.

Final Matches:

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

Boxed Answer:

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