(x+2)(x-4)

Answer 1

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.

Answer 2

(r−1)(r2−2r+3)

Answer 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.

Answer 4

Simplify the polynomial expression (xy−2)(x2+1)

Answer 5

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.