(x+2)(x-4)
To expand the expression (x+2)(x-4), we will use the distributive property:
(x+2)(x-4) = x(x-4) + 2(x-4)
Now, simplify each term:
= x^2 - 4x + 2x -8
Combine like terms:
= x^2 - 2x - 8
Therefore, (x+2)(x-4) expands to x^2 - 2x - 8.
(r−1)(r2−2r+3)
To expand the expression (r-1)(r^2 - 2r + 3), we will use the distributive property:
(r-1)(r^2 - 2r + 3) = r(r^2 - 2r + 3) - 1(r^2 - 2r + 3)
Now, simplify each term:
= r^3 - 2r^2 + 3r - r^2 + 2r - 3
Combine like terms:
= r^3 - 2r^2 - r^2 + 3r + 2r - 3
= r^3 - 3r^2 + 5r - 3
Therefore, (r-1)(r^2 - 2r + 3) expands to r^3 - 3r^2 + 5r - 3.
Simplify the polynomial expression (xy−2)(x2+1)
First, we'll expand the expression using the distributive property:
(xy - 2)(x^2 + 1) = xy(x^2 + 1) - 2(x^2 + 1)
= x^3y + xy - 2x^2 - 2
Therefore, the simplified form of the polynomial expression (xy - 2)(x^2 + 1) is x^3y + xy - 2x^2 - 2.
To expand the expression (x+2)(x-4), we can use the FOIL method, which stands for First, Outer, Inner, and Last.
First, we multiply the first terms of each binomial:
(x)(x) = x^2
Outer, we multiply the outer terms of each binomial:
(x)(-4) = -4x
Inner, we multiply the inner terms of each binomial:
(2)(x) = 2x
Last, we multiply the last terms of each binomial:
(2)(-4) = -8
Now, we can add all the resulting terms together:
x^2 - 4x + 2x - 8
Finally, we can combine like terms:
x^2 - 2x - 8
So, (x+2)(x-4) expands to x^2 - 2x - 8.
To simplify the expression (x+2)(x-4), you can use the distributive property of multiplication over addition. According to this property, when you multiply two binomials, you need to multiply each term in the first binomial by each term in the second binomial, and then combine like terms, if any.
In this expression, (x+2) is the first binomial, and (x-4) is the second binomial. To multiply them, we multiply each term in the first binomial by each term in the second binomial:
(x+2)(x-4) = x(x) + x(-4) + 2(x) + 2(-4)
Now, simplify each term:
x(x) = x^2
x(-4) = -4x
2(x) = 2x
2(-4) = -8
Combine the terms:
x^2 - 4x + 2x - 8
-4x + 2x = -2x, so the expression becomes:
x^2 - 2x - 8
Therefore, the simplified form of (x+2)(x-4) is x^2 - 2x - 8.