Hanson Garrett
01/19/2024 · High School
FMU Question 7 Simplify \( 4 a c-3 a c d-7 a c-7 c+4 a c d \) by combining like terms and then factorising the expression.
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Step-by-step Solution
To simplify the expression \( 4ac - 3acd - 7ac - 7c + 4acd \), we will first combine like terms.
1. **Combine like terms:**
- The terms involving \( ac \) are \( 4ac - 7ac \) which simplifies to \( -3ac \).
- The terms involving \( acd \) are \( -3acd + 4acd \) which simplifies to \( acd \).
- The term \( -7c \) remains as it is.
So, we can rewrite the expression as:
\[
-3ac + acd - 7c
\]
2. **Rearranging the expression:**
We can rearrange it for clarity:
\[
acd - 3ac - 7c
\]
3. **Factor out common factors:**
We can factor out \( c \) from the last two terms:
\[
c(ad - 3a - 7)
\]
Thus, the simplified and factored form of the expression \( 4ac - 3acd - 7ac - 7c + 4acd \) is:
\[
c(ad - 3a - 7)
\]
Quick Answer
The simplified and factored form is \( c(ad - 3a - 7) \).
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