multiply
x (x+y+2)
(-6 -x) (6+x)
(-y^2 +2) (y^2-3)
I will do one...third one.
(-y^2 +2) (y^2-3)
using the FOIL method
(-y^2*y^2 +2*(-3) +2y^2-6)
-y^4+2y^2 -6 + 2y^2 -6 and combine the negative sixes, and they y^2 terms.
x^2 + xy +2x
-36-12x-x^2 or -(x^2 + 12x +36)
-y^4 + 5y^2 -6 or-(y^4 - 5y^2 + 6)
To multiply algebraic expressions such as the ones provided, you can use the distributive property and combine like terms. Here's how to multiply each expression step by step:
1. x (x+y+2):
Start by distributing the x to each term inside the parentheses:
x * x + x * y + x * 2
This simplifies to:
x^2 + xy + 2x
So, x (x+y+2) equals x^2 + xy + 2x.
2. (-6 - x) (6 + x):
Again, distribute each term in the first parentheses (-6 - x) to the terms in the second parentheses (6 + x):
(-6) * (6) + (-6) * (x) + (-x) * (6) + (-x) * (x)
Simplify each multiplication:
-36 - 6x - 6x - x^2
Combine like terms:
-36 - 12x - x^2
So, (-6 - x) (6 + x) equals -36 - 12x - x^2.
3. (-y^2 + 2) (y^2 - 3):
Again, distribute each term in the first parentheses (-y^2 + 2) to the terms in the second parentheses (y^2 - 3):
(-y^2) * (y^2) + (-y^2) * (-3) + (2) * (y^2) + (2) * (-3)
Simplify each multiplication:
-y^4 + 3y^2 + 2y^2 - 6
Combine like terms:
-y^4 + 5y^2 - 6
So, (-y^2 + 2) (y^2 - 3) equals -y^4 + 5y^2 - 6.