Algebraic Expressions
Find the value of the following algebraic expression when x = 2 and y = -3.
3x-4y
3x-4y = 3(2) - 4(-3) = 6 + 12 = 18
Solve the following equation for x.
3x-5 = 16
x=7
The following is the formula for the area of a triangle. Solve the formula for height h.
A = 1/2bh
h = 2A/b
Add the following two polynomials.
4x^2+5x+1 \text{ and } 7x^2-9x+4
11x^2-4x+5
Completely factor the following.
x^2+5x+6
x^2+5x+6 = (x+2)(x+3)
Simplify the following algebraic expression.
5(x-y)-(x+y)
4x-6y
Solve the following equation for x.
-7 = -5x + 9
x = 16/5
The following is the formula for compound interest. Solve the formula for P.
A = P + Prt
P = A/(1+rt)
Subtract 3x^2+7x-1 from 7x^2-2x-4 .
4x^2-9x-3
Completely factor the following.
3x^4+15x^3-21x^2
3x^2(x^2+5x-7)
Simplify the following algebraic expression.
2(6m - 7n) - 5(3m-4n)
-3m+6n
Solve the following equation for x.
2(x+3) + 6(x-4) = 5(x-9)
x=-9
The following is the formula for the area of a trapezoid. Solve the formula for b_1 .
A = 1/2 h(b_1 + b_2)
b_1 = (2A - hb_2)/h
Find the indicated sum:
(-4x^2y + xy^2)+(7x^2y-9xy^2)+(5x^2y-4xy^2)
8x^2y - 12xy^2
Completely factor the following.
4x^5+12x^4-40x^3
4x^3(x-2)(x+5)
Convert the following phrase into an algebraic expression. Let n be the number in question.
"3 times the sum of a number and 2"
3(n+2)
Solve the following equation for x.
(x-2)/3 + (x+1)/8 = 5/6
x=3
The following is the formula for an ellipse, centered at (0,0). Solve the formula for x.
x/a + y/b = 1
x = (ab-ay)/b
Distribute the following.
(3x+2)(5x-7)
15x^2-11x-14
Completely factor the following.
ab^2-4b^2+3a-12
(a-4)(b^2+3)
Sonya has n nickles and d dimes. Express this amount of money in cents.
Each nickel is worth 5 cents and each dime is worth 10 cents. We represent the amount in cents by 5n + 10d.
Solve the following for x.
x + (2x-3)/9 - 2 = (2x+1)/3
x= 24/5
Solve the following equation for the indicated variable.
(y+1)(a-3) = x-2 \text{ for }y
y = (x-a+1)/(a-3)
Distribute the following.
(3 + 2sqrtx)^2
9 + 12sqrtx + 4x
Completely factor the following.
16x^4-81y^4
(4x^2+9y^2)(2x+3y)(2x-3y)