Which of the following equivalent form of the expression `(6-5x) (15x -11)` ?

Options

A. `-75x ^(2) + 35 x -66`
B. `-75 x ^(2) + 145x -66`
C. `90 x^(2)-141x +35`
D. `90x ^(2) +9x +55`

Explanation

To find an equivalent form of the expression \((6 - 5x)(15x - 11)\), we will use the distributive property (also known as the FOIL method for binomials) to expand the expression step by step.

### Step 1: Distribute the first term of the first bracket
Multiply \(6\) by each term in the second bracket:
\[ 6 \cdot 15x = 90x \]
\[ 6 \cdot (-11) = -66 \]

### Step 2: Distribute the second term of the first bracket
Now, multiply \(-5x\) by each term in the second bracket:
\[ -5x \cdot 15x = -75x^2 \]
\[ -5x \cdot (-11) = 55x \]

### Step 3: Combine all the terms
Now, we combine all the results from Steps 1 and 2:
\[ -75x^2 + 90x + 55x - 66 \]

### Step 4: Combine like terms
Combine the \(x\) terms:
\[ 90x + 55x = 145x \]

### Final Expression
Putting it all together, we have:
\[ -75x^2 + 145x - 66 \]

Thus, the equivalent form of the expression \((6 - 5x)(15x - 11)\) is:
\[ -75x^2 + 145x - 66 \]