Answer/Step-by-step explanation:
A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]
[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)
[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)
B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]
[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)
[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]
[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]
Combine like terms
[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (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
