Question

complete the table to find the product.
1
$(-3x - 8)^2$

	-3x	-8
-8

final answer
2
$(6x^2 + 14)(2x - 1)$

final answer

Explanation:

Problem 1: \((-3x - 8)^2\)

Step 1: Fill the table (First row, first column)

Multiply \(-3x\) and \(-3x\): \((-3x)\times(-3x) = 9x^2\)

Step 2: Fill the table (First row, second column)

Multiply \(-3x\) and \(-8\): \((-3x)\times(-8) = 24x\)

Step 3: Fill the table (Second row, first column)

Multiply \(-8\) and \(-3x\): \((-8)\times(-3x) = 24x\)

Step 4: Fill the table (Second row, second column)

Multiply \(-8\) and \(-8\): \((-8)\times(-8) = 64\)

Step 5: Sum the terms

Add all the products: \(9x^2 + 24x + 24x + 64 = 9x^2 + 48x + 64\)

Step 1: Fill the table (First row, first column)

Multiply \(6x^2\) and \(2x\): \(6x^2\times2x = 12x^3\)

Step 2: Fill the table (First row, second column)

Multiply \(6x^2\) and \(-1\): \(6x^2\times(-1) = -6x^2\)

Step 3: Fill the table (Second row, first column)

Multiply \(14\) and \(2x\): \(14\times2x = 28x\)

Step 4: Fill the table (Second row, second column)

Multiply \(14\) and \(-1\): \(14\times(-1) = -14\)

Step 5: Sum the terms

Add all the products: \(12x^3 - 6x^2 + 28x - 14\)

Answer:

The table entries are \(9x^2\), \(24x\), \(24x\), \(64\) and the final answer is \(9x^2 + 48x + 64\)

Problem 2: \((6x^2 + 14)(2x - 1)\)