Let's solve the given expression step-by-step:
We need to calculate:
[tex]\[ 9 - \left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right)\left(\frac{7}{4} a - \frac{3}{2} b\right) \][/tex]
Step 1: Define the expressions
First, let's denote the given expressions as:
[tex]\[ \text{Expression 1: } \frac{7}{4} a^2 - a b + \frac{2}{3} b^3 \][/tex]
[tex]\[ \text{Expression 2: } \frac{7}{4} a - \frac{3}{2} b \][/tex]
Step 2: Multiply the expressions
Next, we need to multiply these two expressions:
[tex]\[ \left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right) \left(\frac{7}{4} a - \frac{3}{2} b\right) \][/tex]
This gives us the product:
[tex]\[ \left(\frac{7}{4} a - \frac{3}{2} b\right) \left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right) \][/tex]
Step 3: Substitute the product into the final expression
Now, we substitute the product back into the final expression we need to calculate:
[tex]\[ 9 - \left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right)\left(\frac{7}{4} a - \frac{3}{2} b\right) \][/tex]
Step 4: Write the final result
Therefore, the final result of the expression is:
[tex]\[ 9 - \left(\left(\frac{7}{4} a - \frac{3}{2} b\right)(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3)\right) \][/tex]
Thus, we have:
[tex]\[ \left(\frac{7}{4} a - \frac{3}{2} b\right)\left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right) \][/tex]
[tex]\[ 9 - \left(\left(\frac{7}{4} a - \frac{3}{2} b\right)\left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right)\right) \][/tex]
Explicitly, the intermediate and final results are:
[tex]\[ \left(\frac{7}{4} a - \frac{3}{2} b\right)\left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right) \][/tex]
[tex]\[ 9 - \left(\left(\frac{7}{4} a - \frac{3}{2} b\right)\left(\frac{7}{4} a^2 - a b + \frac{2}{3} b^3\right)\right) \][/tex]
