Questions: Divide and check (28 w^7 f^8 - 12 w^5 f^6 + 12 w^2 f^3) / (4 w^2 f)

Transcript text: Divide and check \[ \frac{28 w^{7} f^{8}-12 w^{5} f^{6}+12 w^{2} f^{3}}{4 w^{2} f} \]

Solution

Solution Steps

To solve the given expression, we need to divide each term in the numerator by the denominator. This involves simplifying the coefficients and reducing the powers of the variables \( w \) and \( f \) by subtracting the exponents in the denominator from those in the numerator.

Step 1: Simplify the Expression

We start with the given expression: \[ \frac{28 w^{7} f^{8} - 12 w^{5} f^{6} + 12 w^{2} f^{3}}{4 w^{2} f} \]

Step 2: Divide Each Term by the Denominator

We divide each term in the numerator by the denominator \(4 w^{2} f\): \[ \frac{28 w^{7} f^{8}}{4 w^{2} f} - \frac{12 w^{5} f^{6}}{4 w^{2} f} + \frac{12 w^{2} f^{3}}{4 w^{2} f} \]

Step 3: Simplify Each Term

Simplify each term individually: \[ \frac{28 w^{7} f^{8}}{4 w^{2} f} = 7 w^{5} f^{7} \] \[ \frac{12 w^{5} f^{6}}{4 w^{2} f} = 3 w^{3} f^{5} \] \[ \frac{12 w^{2} f^{3}}{4 w^{2} f} = 3 f^{2} \]

Step 4: Combine the Simplified Terms

Combine the simplified terms to get the final expression: \[ 7 w^{5} f^{7} - 3 w^{3} f^{5} + 3 f^{2} \]