-45y^2+40y

To factor the expression -45y^2 + 40y, we first need to find the greatest common factor of the coefficients and variables. In this case, the greatest common factor of -45 and 40 is 5, and the greatest common factor of y^2 and y is y.

So, we can factor out 5y from the expression:

-45y^2 + 40y
= 5y (-9y + 8)

Therefore, the factored form of the expression -45y^2 + 40y is 5y (-9y + 8).

y^2+11y+24

To factor the expression y^2 + 11y + 24, we need to find two numbers that multiply to 24 and add up to 11. The two numbers that meet these criteria are 3 and 8.

Therefore, we can rewrite the expression as:

y^2 + 3y + 8y + 24

Now, we can group the terms and factor by grouping:

y(y + 3) + 8(y + 3)
(y + 3)(y + 8)

Therefore, the factored form of the expression y^2 + 11y + 24 is (y + 3)(y + 8).

y^2-7y-60

To factor the expression y^2 - 7y - 60, we need to find two numbers that multiply to -60 and add up to -7. The two numbers that meet these criteria are -12 and 5.

Therefore, we can rewrite the expression as:

y^2 - 12y + 5y - 60

Now, we can group the terms and factor by grouping:

y(y - 12) + 5(y - 12)
(y - 12)(y + 5)

Therefore, the factored form of the expression y^2 - 7y - 60 is (y - 12)(y + 5).

(3y^4+5)(5y^7+4)

To factor the expression (3y^4 + 5)(5y^7 + 4), we can use the distributive property to multiply the terms from each expression together.

(3y^4 + 5)(5y^7 + 4)
= 3y^4 * 5y^7 + 3y^4 * 4 + 5 * 5y^7 + 5 * 4
= 15y^11 + 12y^4 + 25y^7 + 20

Therefore, the factored form of the expression (3y^4 + 5)(5y^7 + 4) is 15y^11 + 12y^4 + 25y^7 + 20.