Q: Multiply -9m(2m2 + 6m – 1)
A: When adding and subtracting polynomials, you can only combined like terms. This is not the case with multiplication. You can multiply unlike terms together.
-9m(2m2 + 6m – 1)
In this problem the whole quantity in the parentheses is being multiplied by -9m. So, -9m needs to multiply each term:
-9m(2m2 + 6m – 1) = -9m*2m2 + -9m*6m + -9m*-1
1: Subtract: (-4y2-3y+8) – (2y2-6y+2)
A: Here we are just asked to clean things up and combine like terms: basically, add apples with apples and oranges with oranges, but don’t accidentally add apples with oranges!
y2 terms get combined with y2 terms
y terms get combined with y terms
constants (lone numbers) get combined with constants
So, let’s use color to highlight the like terms:
(-4y2-3y+8) – (2y2-6y+2)
How many total y2 terms do you have? -4y2 – 2y2 = -6y2
How many total y terms do you have? -3y – -6y = -3y+6y = 3y
How many total constant terms do you have? 8 – +2 = 8 – 2 = 6
Did we forget anyone? Did anyone not have a match that we need to bring along? Nope! Everyone from both sets of parentheses is accounted for!
So, final answer:
(-4y2-3y+8) – (2y2-6y+2) = -6y2 + 3y + 6
Q: Add: (3x3+2x2-5x) + (-4x3-x2-8x)
A: Here we are just asked to clean things up and combine like terms: basically, add apples with apples and oranges with oranges, but don’t accidentally add apples with oranges!
x3 terms get added with x3 terms
x2 terms get added with x2 terms
x terms get added with other x terms
So, let’s use color to highlight the like terms:
(3x3+2x2-5x) + (-4x3–x2-8x)
How many total x3 terms do you have? 3x3+ -4x3 = -1x3
How many total x2 terms do you have? 2x2+–x2 = 1x2
How many total x terms do you have? -5x+ -8x = -13x
Did we forget anyone? Did anyone not have a match that we need to bring along? Nope! Everyone from both sets of parentheses is accounted for!
So, final answer:
(3x3+2x2-5x) + (-4x3–x2-8x) = -1x3 + 1x2 – 13x
Since we tend not to write the “1”, you might see the answer displayed as:
–x3 + x2 – 13x
