Find a number that evenly divides each term of the expression.
For each expression, divide the numerator and denominator by their greatest common factor.
For each of a list of algebraic expressions, find one or more common factors and factorise the expression.
11 x P x Q x R = 11PQR
Some expressions can't be factorised, and you have to use other methods to solve the equation.
A = 4x + 12 = 4x + 4 × 3 = 4(x + 3)
example x5 + 6x4 + 9x3 To factor this expression, see if each "piece" of the expression has a variable in common. In this case, each piece has an X in common. Now we factor out the smallest exponent of X that we see in the expression. x3(x2+6x +9) You could factor the x squared +6x +9 also, into (x + 3)(x+3)
"Greatest common factor of an expression" is meaningless."Greatest common factor of two or more numbers" is the largest integerthat can divide evenly into each of the numbers.
In both cases, you may be able to cancel common factors, thus simplifying the expression.
2(15-2n) Look for the greatest common factor of 30 and -4n. Put it out front, then divide each term by this number to get the expression in the parentheses. 30/2 = 15, -4n/2 = -2n.
4x + 32 = 4(x + 8)
Take out the common factor, which in this case is 4x2. Divide each of the terms by this common factor. 12x2 - 4x3 = 4x2(3+x)
Make note that a term doesn't have to be a number. It can be the expression, like (3x - 6). In order to consider a term of the factorization of the term to be the factor, it must be prime. Therefore, we call each factor in a term "prime factor". Here is the example: 2x + 6 has a factor of 2. Then, we can factor out 2x + 6 to get 2(x + 3)
It is x^2 -4 = (x-2)(x+2) when factored and it is the difference of two squares
Remove common factors. The common factor is 3x. Then since you must keep the expression constant you put in parentheses what you must multiply 3x by to get each of the original parts of the expression. So the answer must be 3x+3xy=3x(1+y).
Replace each variable in the expression by its value and then find the value of the expression.
Factor each of the denominators. Make up an expression that includes all of the factors in the denominators. Example (using "^" for powers):If you have denominators (x^2 - 1), (x-1)^2 and (x+1), factor the first expression, to get denominators: (x+1)(x-1), (x-1)^2 and (x+1). Taking each factor that appears at least once, you get the common denominator: (x+1)(x-1)^2. Note: If a factor, as in this case x-1, appears more than once in one of the expressions, you need to use the highest power.
Replace each variables in the algebraic expression by its [known] value and calculate the value (ie evaluate) of the algebraic expression.
Start by factoring each part. If you find a common factor in the numerator and the denominator, eliminate it in both.
Evaluating the expression.
That is sometimes known as EVALUATING the expression.