simplify: $3(\frac{7}{3}{x}^2-27x+14)-7(x^2+8x-11)$

The correct answer is −137x + 119.

To simplify the given algebraic expression, we use the distributive property to expand both sets of parentheses and then combine like terms.

Step 1: State the original expression.

$3(\frac{7}{3}{x}^2-27x+14)-7(x^2+8x-11)$

Step 2: Distribute the constant factors.

First, multiply 3 by each term inside the first set of parentheses:

$3\left(\frac{7}{3}{x}^2\right)-3\left(27x\right)+3\left(14\right)=7x^2-81x+42$

Next, multiply -7 by each term inside the second set of parentheses:

$-7\left(x^2\right)-7\left(8x\right)-7(-11)=-7x^2-56x+77$

Step 3: Combine all terms into a single expression.

$7x^2-81x+42-7x^2-56x+77$

Step 4: Group like terms.

$(7x^2-7x^2)+(-81x-56x)+(42+77)$

Step 5: Perform the final simplification.

• $7x^2-7x^2=0$
• $-81x-56x=-137x$
• $42+77=119$

Putting these components together, the simplified result is:

$-137x+119$