### Algebra

Algebra is based on the operations of arithmetic and on the concept of an unknown quantity, or variable. Letters such as x or n are used to represent unknown quantities. For example, suppose A has 5 more pencils than B, then the number of pencils that A has is B+5.

### Simplifying Algebraic Equations

When working with algebraic expressions, it is necessary to simplify them by factoring or combining like terms. For example, the expression 6x+5x is equivalent to (6+5)x, or 11x. In the expression 9x-3y, 3 is a factor common to both the terms: 9x-3y = 3(3x-y). In the expression 5x^{2}+6y, there are no like terms and no common factors.

If there are common factors in the numerator and denominator of an expression, they can be divided out, provided that they are not equal to zero.

To multiply two algebraic expressions, each term of one expression is multiplied by each term of the other expression. For example:

(3x-4)(9y+x) = 3x(9y+x) - 4(9y+x) = (3x)(9y) + (3x)(x) + (-4)(9y) + (-4)(x) = 27xy + 3x^{2} -36y - 4x

An algebraic expression can be evaluated by substituting values of the unknowns in the expression. For example, if x=3 and y=-2, then 3xy-x^{2}+y can be evaluated as 3(3)(-2) - (3)^{2} + (-2) = -18 - 9 - 2 = -29.