Question

Plz help i dont understand using a table. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)

A) (4x2 – 4x)(x2 – 4)
B) (x2 + x – 2)(4x2 – 8x)

Answer 1

A. 4x⁴ - 4x³ - 16x² - 16x

B. 4x⁴ - 4x³ - 16x² + 16x

Explanation:

If you want to find the product of 2 binomial (or even polynomial) expressions, you simply need to multiply every term in one expression by every term in the other:

A.

(4x² - 4x)(x² - 4) = 4x²(x²) + 4x²(-4) - 4x(x²) - 4x(4)

= 4x⁴ - 16x² - 4x³ - 16x

= 4x⁴ - 4x³ - 16x² - 16x

`\left[\begin{array}{ccc}*&4x^(2)&-4x\\x^(2)&4x^(4)&-4x^(3)\\-4&-16x^(2)&-16x\end{array}\right]`

B.

(x² + x - 2)(4x² - 8x) = x²(4x²) + x(4x²) - 2(4x²) + x²(-8x) + x(-8x) - 2(-8x)

= 4x⁴ + 4x³ - 8x² - 8x³ - 8x² + 16x

= 4x⁴ - 4x³ - 16x² + 16x

`\left[\begin{array}{cccc}*&x^(2)&x&-2\\4x^(2)&4x^(4)&4x^(3)&-8x^(2)\\-4x&-4x^(3)&-4x^(2)&8x\end{array}\right]`

Descending order simply means the powers must be largest first and smallest last.