Question

use the box method to distribute and simplify $(-4 - 4x^2 + 3x)(5x - 4)$. drag and drop the terms to the correct locations of the table.
$(-4 - 4x^2 + 3x)(5x - 4)$
rows: 0
columns: 0
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

First, rewrite the first polynomial in standard form: \(-4x^2 + 3x - 4\). The second polynomial is \(5x - 4\). We will create a box (table) with 3 rows (corresponding to the terms of \(-4x^2 + 3x - 4\)) and 2 columns (corresponding to the terms of \(5x - 4\)).

Step 1: Multiply \(-4x^2\) by each term in \(5x - 4\)

• Multiply \(-4x^2\) by \(5x\): \(-4x^2 \times 5x = -20x^3\)
• Multiply \(-4x^2\) by \(-4\): \(-4x^2 \times (-4) = 16x^2\)

Step 2: Multiply \(3x\) by each term in \(5x - 4\)

• Multiply \(3x\) by \(5x\): \(3x \times 5x = 15x^2\)
• Multiply \(3x\) by \(-4\): \(3x \times (-4) = -12x\)

Step 3: Multiply \(-4\) by each term in \(5x - 4\)

• Multiply \(-4\) by \(5x\): \(-4 \times 5x = -20x\)
• Multiply \(-4\) by \(-4\): \(-4 \times (-4) = 16\)

Now, we combine like terms:

• The \(x^3\) term: \(-20x^3\)
• The \(x^2\) terms: \(16x^2 + 15x^2 = 31x^2\)
• The \(x\) terms: \(-12x - 20x = -32x\)
• The constant term: \(16\)

Putting it all together, the simplified form is \(-20x^3 + 31x^2 - 32x + 16\).

To fill the box (table):

	\(5x\)	\(-4\)
\(3x\)	\(15x^2\)	\(-12x\)
\(-4\)	\(-20x\)	\(16\)

Then, combine the terms inside the box: \(-20x^3 + (16x^2 + 15x^2) + (-12x - 20x) + 16 = -20x^3 + 31x^2 - 32x + 16\)

Answer:

The simplified form using the box method is \(\boldsymbol{-20x^3 + 31x^2 - 32x + 16}\). The table (box) should be filled as follows:

	\(5x\)	\(-4\)
\(3x\)	\(15x^2\)	\(-12x\)
\(-4\)	\(-20x\)	\(16\)