Question

if y1=x^2+3x-1 and y2=x-5,
find: a. y1+y2
b. y1-y2
c. y1(y2)

Answer 1

y1 = x^2 + 3x - 1
y2 = x - 5
for y1 - y2, combine similar terms,, for terms with same variables, add their numerical coefficients (number before the variable) and copy the variable:
x^2 + 3x - 1 -(x - 5)
x^2 + 3x - 1 - x + 5
x^2 + 3x - x - 1 + 5 *i just rearrange the terms*
x^2 + 2x + 4

for y1(y2), distribute each term:
(x^2 + 3x - 1)(x - 5)
to distribute, multiply x^2 by x plus x^2 times -5, plus 3x times x plus 3x times -5, and so on:
(x^2)*x + (-5)x^2 + 3x^2 - 15x - x + 5
now simplify this by combining similar terms.

Answer 2

Alright. a. y1+y2 should be set up as follows:
(x^2+3x-1)+(x-5), which equates to
x^2+4x-6
You just combine the like terms.

b. (x^2+3x-1)-(x-5)
For this one you need to distribute the negative, to get x^2+3x-1-x+5, then combine like terms.

c. (x-5)(x^2+3x-1)= x^3+3x^2-x-5x^2-15x+5. Combine like terms.