Algebra and trigonometry fundamentals

Algebra, Trig

Perform the indicated operation and simplify completely: (x + 10)(x^2 + 9x - 8)

(x + 10)(x^2 + 9x - 8) = x^3 + 9x^2 -- 8x + 10x^2 + 90x -- 80 = x^3 + 19x^2 +82x --

Perform the indicated operation and simplify completely:

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9)

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9) = (5x + 5 + 5x + 13) / (5x + 9)

= (10x + 18) / (5x + 9) = 2(5x + 9) / (5x + 9) = 2

Perform the indicated operation and simplify completely:

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x)

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x) = 8x^6 + 7x^3 + 3x + 3x^6 + 5x^3 -- 5x

= 11x^6 + 12x^3 -- 2x

Perform the indicated operation and simplify completely: (x - 3)^

3)^3 = (x -- 3)(x -- 3)(x -- 3) = (x^2 -- 3x -- 3x + 9)(x -- 3) = (x^2 -- 6x + 9)(x -- 3)

= x^3 -- 3x^2 -- 6x^2 + 18x + 9x -- 27 = x^3 -- 9x^2 + 27x -

Factor: 4x^2-9y^2 completely

4x^2 -- 9y^2 = (2x + 3y)(2x -- 3y)

Factor: 4x - 40 completely

4x -- 40 = 4(x -- 10)

Perform the indicated operation and simplify completely: (x + 11)(x -11)

(x + 11)(x -11) = x^2 + 11x -- 11x -- 121 = x^2 -- 121

8. Perform the indicated operation and simplify completely:

(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2)

(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2) = x^3 + 3xy -- 8y^2 -- 6x^3 -- 8xy -- y^2

= -5x^3 -- 5xy -- 9y^2

9. Perform the indicated operation and simplify completely:

[2x / (4x + 2)] * [(6x + 3) / 5)]

[2x / (4x + 2)] * [(6x + 3) / 5)] = (12x^2 + 6x) / (20x + 10) = [6x (2x + 1)] / [10(2x + 1)]

= 6x / 10 = 2(3x) / 2(5) = 3x / 5

10. Factor: x (x + 12) + 11(x + 12) completely x (x + 12) + 11(x + 12) = (x + 11)(x + 12)

11. Factor: x^2 + 10x + 21 completely x^2 + 10x + 21 = (x + 7)(x + 3)