−4y^8(10y^10−5y^6+2y^3)

To solve this, we will distribute the -4y^8 to each term inside the parentheses:

-4y^8 * 10y^10 = -40y^18
-4y^8 * -5y^6 = 20y^14
-4y^8 * 2y^3 = -8y^11

Therefore, the simplified expression is:

-40y^18 + 20y^14 - 8y^11

(2y^3+10)(3y^5+4)

To simplify this expression, we will distribute each term from the first set of parentheses to each term in the second set:

(2y^3 + 10)(3y^5 + 4)

First distribute 2y^3 to each term:

2y^3 * 3y^5 = 6y^8
2y^3 * 4 = 8y^3

Next, distribute 10 to each term:

10 * 3y^5 = 30y^5
10 * 4 = 40

Combine the like terms:

6y^8 + 8y^3 + 30y^5 + 40

Therefore, the simplified expression is:

6y^8 + 30y^5 + 8y^3 + 40

(5y^3+8)(−4y^6+2)

To simplify the expression (5y^3 + 8)(-4y^6 + 2), we will distribute each term from the first set of parentheses to each term in the second set:

First, distribute 5y^3 to each term:

5y^3 * -4y^6 = -20y^9
5y^3 * 2 = 10y^3

Next, distribute 8 to each term:

8 * -4y^6 = -32y^6
8 * 2 = 16

Combine the like terms:

-20y^9 + 10y^3 - 32y^6 + 16

Therefore, the simplified expression is:

-20y^9 - 32y^6 + 10y^3 + 16

(−6y+7)(5y+5)

To simplify the expression (-6y + 7)(5y + 5), we will distribute each term from the first set of parentheses to each term in the second set:

First distribute -6y to each term:

-6y * 5y = -30y^2
-6y * 5 = -30y

Next, distribute 7 to each term:

7 * 5y = 35y
7 * 5 = 35

Combine the like terms:

-30y^2 - 30y + 35y + 35

Simplify by combining like terms further:

-30y^2 + 5y + 35

Therefore, the simplified expression is:

-30y^2 + 5y + 35

(3y+4)(4y+5)

To simplify the expression (3y + 4)(4y + 5), we will distribute each term from the first set of parentheses to each term in the second set:

First distribute 3y to each term:

3y * 4y = 12y^2
3y * 5 = 15y

Next, distribute 4 to each term:

4 * 4y = 16y
4 * 5 = 20

Combine the like terms:

12y^2 + 15y + 16y + 20

Simplify by combining like terms further:

12y^2 + 31y + 20

Therefore, the simplified expression is:

12y^2 + 31y + 20