### Questions

3. What must be added to:

(a) [tex]$x - y + 4z$[/tex] to get [tex]$5x - 4y + 8z$[/tex]?

(b) [tex][tex]$a - 2b + 6$[/tex][/tex] to get [tex]$3a - b + 5$[/tex]?

(c) [tex]$2x + 3y - z$[/tex] to get [tex][tex]$x - y + z$[/tex][/tex]?

(d) [tex]$a^3 + b^3$[/tex] to get [tex]$a^3 + b^3 + 3a^2b + 3ab^2$[/tex]?

4. What must be subtracted from:

(a) [tex][tex]$a^2 + 2ab + b^2$[/tex][/tex] to get [tex]$a^2 + b^2$[/tex]?

(b) [tex]$11x^2 + 16xy - 5y^2$[/tex] to get [tex][tex]$x^2 + y^2$[/tex][/tex]?

(c) [tex]$a^2 - 9ab + 11b^2$[/tex] to get [tex]$5ab - a^2 - b^2$[/tex]?

(d) [tex]$a^3 + 3a^2b + 3ab^2 + b^3$[/tex] to get [tex][tex]$a^3 + b^3$[/tex][/tex]?

5.

(a) From the sum of [tex]$-6x^2 + 7xy - 4y^2$[/tex] and [tex]$6x^2 + 9xy - 9y^2$[/tex], subtract [tex][tex]$4x^2 - 10xy - 8y^2$[/tex][/tex].