Question

Fill in the blanks (ASAP- 30 points, must answer all)

19m^2n - 114mn^2 = 19mn (_____________ - ______________)

24p^3t + 60p^3 = ____________ (2t + 5)

5wz + 25w^2z + 35w^3z = 5wz ( ______________ + __________ - __________)

Answer 1

1) (m - 6n)

2) 12p³

3) (1 + 5w - (-7w²))

Explanation:

19m^2n - 114mn^2

19mn(m) - 19mn(6n)

19mn(m - 6n)

24p^3t + 60p^3 =

12p³(2t) + 12p³(5)

12p³(2t + 5)

5wz + 25w^2z + 35w^3z

5wz(1) + 5wz(5w) + 5wz(7w²)

5wz(1 + 5w + 7w²)

5wz(1 + 5w - (-7w²))

Answer 2

`(m-6n)`

`12p^3`

`19m^(2)n-114mn^2=19mn\\19mn(m-6n)=19mn \\`

`24p^(3t)+60p^3=(*********)(2t+5)`

`24p^(3t)+60p^3\\24\left(p^t\right)^3+60p^3\\2\cdot \:12\left(p^t\right)^3+5\cdot \:12p^3\\12\left(2\left(p^t\right)^3+5p^3\right)\\12\left(2p^(3t)+5p^3\right)\\12(2p^3 p^t+5p^3)\\12p^3(2 p^t+5)`

`5wz\:+\:25w^2z\:+\:35w^3z\:=\:5wz\\5wz+25w^2z+35w^3z-5wz=5wz-5wz\\35zw^3+25zw^2=0\\5zw^2\left(7w+5\right)=0`

Considering just the LHS:

`5wz\:+\:25w^2z\:+\:35w^3z\:\\5wz(1+5w+7w^2)\\5wz(1+5w-(-7w^2))`