Question

3. Are the two products the same when you multiply them with the table method? (1 point)

Multiplying Using the Distributive Property:
4. Multiply the two polynomials using the distributive property. (4 points: 2 points for each product)
A) (4x2 - 4x)(x2 - 4)
B)(x2+x-2)(4x2 - 8x)
5. Are the two products the same when you multiply them horizontally? (1 point)

Answer 1

Distribute and multiply term-wise.

Explanation:

A) (4x² - 4x)(x² - 4)

Distribute it and multiply them.

We have:
`$ (4x^2)(x^2) - 4x^2(4) - 4x(x^2) + 4x(4) $`

`$ = 4x^4 - 4x^3 - 16x^2 + 16 $`

This is the product after distribution.

B) (x² + x - 2)(4x² - 8x)

Using the same method as above we get:

`$ x^2(x^2) - x^2(8x) + x(4x^2) - x(8x) - 2(4x^2) + 2(8x) $`

`$ = 4x^4 - 8x^3 + 4x^3 - 8x^2 - 8x^2 + 16x $`

`$ = 4x^4 - 4x^3 - 16x^2 + 16x $` is the required answer.