Question

1. Multiply the following polynomials to write an equivalent expression.

Part A: -7x2y2 (8x2y – 5xy + 11xy2 – 31)
Part B: (t3 – 5t) E+2 – 3t)
Part C: (4x2 – 7x + 5)(2x - 5)
Part D: (3m2 - 5m + 2)2

Answer 1

Answer/Step-by-step explanation:

A.
`-7x^2y^2(8x^2y - 5xy + 11xy^2 - 31)`

`-7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31)` (distributive property)

`-56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2` (note: - × - = + and - × + = -)

B.
`((4)/(5)t^3 - 5t)((1)/(4)t^2 - 3t)`

`((4)/(5)t^3)((1)/(4)t^2 - 3t) - 5t((1)/(4)t^2 - 3t)` (distributive property)

`(4*1)/(5*4)t^3*t^2 - (4*3)/(5)t^3*t - (5*1)/(4)t*t^2 + 15t^2`

`(1)/(5)t^5 - (12)/(5)t^3 - (5)/(4)t^3 + 15t^2`

Combine like terms

`(1)/(5)t^5 - (73)/(20)t^3 + 15t^2` (note: -12/5 - 5/4 = -73/20)

C. (4x² - 7x + 5)(2x - 5)

4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)

8x³ - 20x² - 14x² + 35x + 10x - 25

Combine like terms

8x³ - 34x² + 45x - 25

D. (3m² - 5m + 2)²

= (3m² - 5m + 2)(3m² - 5m + 2)

= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)

= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4

Combine like terms

= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4

= 9m⁴ - 30m³ + 37m² - 20m + 4