The factor form `5x(y+z)-7y(y+z)` is

Options

A. `(5x-7y)(y-z)`
B. `(5x-7y)(y+z)`
C. `(5x+7y)(y+z)`
D. `(5x+7y)(y-z)`

Answer

To factor the expression \( 5x(y + z) - 7y(y + z) \), we can follow these steps:

### Step 1: Identify the common factor
The given expression is:
\[ 5x(y + z) - 7y(y + z) \]
We can see that \( (y + z) \) is a common factor in both terms.

### Step 2: Factor out the common factor
We can factor \( (y + z) \) out of the expression:
\[ = (y + z)(5x - 7y) \]

### Step 3: Write the final factored form
Thus, the expression in its factor form is:
\[ (y + z)(5x - 7y) \]

### Conclusion
The factor form of the expression \( 5x(y + z) - 7y(y + z) \) is:
\[ (5x - 7y)(y + z) \]