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/Step-by-step explanation:

A.

(distributive property)

(note: - × - = + and - × + = -)

B.

(distributive property)

Combine like terms

(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

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8