To solve the expression 91y³ ÷ (21y² + 35y + 7y), we will first simplify the denominator and then perform the division.
1. **Combine like terms in the denominator**:
The expression in the denominator is 21y² + 35y + 7y. Let’s combine the terms with y:
21y² + (35y + 7y) = 21y² + 42y
So, now we have:
91y³ ÷ (21y² + 42y)
2. **Factor the denominator**:
We can factor out a common term in the denominator:
21y² + 42y = 21y(y + 2)
So now we rewrite the expression:
91y³ ÷ 21y(y + 2)
3. **Divide the coefficients and simplify the variables**:
Now, we can divide 91y³ by 21y:
Coefficient: 91 ÷ 21 = 4.3333 (which is approximately 4 1/3 or can be expressed as a fraction as 13/3).
Variables: y³ ÷ y = y² (since 3 – 1 = 2)
Putting it all together:
The quotient is approximately (13/3)y² / (y + 2) or 4.3333y² / (y + 2).
4. **Final answer in simplified format**:
The final answer for the quotient of the expression 91y³ ÷ (21y² + 35y + 7y) is:
4.3333y² / (y + 2) or, if preferred, (13/3)y² / (y + 2).