expand and simplify
1. -(y^2-4y+7)(3y^2-5y-3)
2.2(a+b^3
1. -(y^2 - 4y + 7)(3y^2 -5y -3) =
-3y^4 + 5y^3 + 3y^2 + 12y^3 - 20Y^2- 12y -21Y^2 + 35Y + 21 =
-3Y^4 + 17Y^3 - 38Y^2 + 23Y + 21 =
2. 2(a + b^3) = 2a + 2b^3. This one was already simplified.
To expand and simplify an expression, you need to use the distributive property and combine like terms. Let's take a look at each question separately:
1. -(y^2 - 4y + 7)(3y^2 - 5y - 3)
To expand this expression, we need to distribute the negative sign to each term inside the parentheses:
-(y^2 - 4y + 7)(3y^2 - 5y - 3) = -y^2(3y^2 - 5y - 3) + 4y(3y^2 - 5y - 3) - 7(3y^2 - 5y - 3)
Next, we multiply each term inside the parentheses by the corresponding term outside the parentheses:
= -3y^4 + 5y^3 + 3y^2 + 12y^3 - 20y^2 - 12y - 21y^2 + 35y - 21
Now, we can combine like terms:
= -3y^4 + 17y^3 - 38y^2 + 23y - 21
Therefore, the expanded and simplified expression is -3y^4 + 17y^3 - 38y^2 + 23y - 21.
2. 2(a + b^3)
To expand this expression, we distribute the coefficient 2 to each term inside the parentheses:
2(a + b^3) = 2*a + 2*b^3
Next, we can rewrite the expression without the parentheses:
= 2a + 2b^3
This expression is already in its simplified form, as no like terms can be combined further.
Therefore, the expanded and simplified expression is 2a + 2b^3.