To find the value of a numeric expression, determine the order of actions in a given example. For convenience, label it with a pencil over the appropriate signs. Will follow all of these steps in a certain order: the actions in parentheses, exponentiation, multiplication, division, addition, subtraction. The resulting number will be the value of a numeric expression.
Example. Find the value of the expression (34∙10+(489-296)∙8):4-410. Determine the order of action. The first action is run in the inner brackets 489-296=193. Then, multiply 193∙8=1544 34∙10=340. Next activity: 340+1544=1884. Then follow the division 1884:4=461, and then subtract 461-410=60. You have found the value of this expression.
To find the value of trigonometric expressions at a known angle α, the pre - simplify the expression. To do this, apply the appropriate trigonometric formula. Calculate the values of trigonometric functions, substitute them in the example. Follow the steps.
Example. Find the value of the expression 2sin 30 ° ∙cos 30º∙tg 30º∙ctg 30º. Simplify this expression. To do this, use the formula tg α∙ctg α=1. Get: 2sin 30 ° ∙cos 30º∙1=2sin 30 ° ∙cos 30º. It is known that sin 30º=1/2 cos 30º=√3/2. Therefore, 2sin 30 ° ∙cos 30º=2∙1/2∙√3/2=√3/2. You have found the value of this expression.
The value of an algebraic expression depends on the value of the variable. To find the value of algebraic expressions with given variables, simplify the expression. Substitute variable values. Take the appropriate action. In the end, you will receive a number, and that is the value of algebraic expressions with given variables.
Example. Find the value of expression 7(a+y)-3(2a+3y) when a=21 and y=10. Simplify this expression, we get: a–2y. Substitute appropriate values for the variables and calculate: a–2y=21-2∙10=1. This is the value of the expression 7(a+y)-3(2a+3y) when a=21 and y=10.
There are algebraic expressions that have no meaning for some values of the variables. For example, the expression x/(7–a) does not make sense if a=7, since the denominator becomes zero.
Advice 2 : How to simplify an expression in math
Learn how to simplify expressions in math just need to correctly and quickly solve the tasks, different equations. Simplify the expression implies a reduction in the number of actions, which facilitates the calculation and saves time.
Learn how to calculate the degree with the natural indicators. When multiplying degrees with the same grounds get the degree number, the base of which remains the same, and the exponents are added b^m+b^n=b^(m+n). By dividing the degrees with the same bases receive the degree number, the base of which remains the same, and the exponents are subtracted, and the rate of the dividend is subtracted the index divisor of b^m:b^n=b^(m-n). During the construction of the degree in the degree obtained degree number, the base of which remains the same, and the two values are multiplied (b^m)^n=b^(mn)in the exponentiation of products of numbers in this degree is built every multiplier.(abc)^m=a^m*b^m*c^m
Play the polynomials into factors, i.e. imagine them as a product of multiple factors of polynomials and monomials. Take out a common factor of the brackets. Learn the basic formulas of reduced multiplication: the difference of squares, square sums, square differences, sum of cubes, difference of cubes, cube of sum and difference. For example, m^8+2*m^4*n^4+n^8=(m^4)^2+2*m^4*n^4+n^4)^2. These are the basic formulas to simplify expressions. Use the method of separating the complete square trinomial of the form ax^2+bx+c.
As often as possible, reduce fractions. For example, (2*a^2*b)/(a^2*b*c)=2/(a*c). But remember that you can cut only the multipliers. If the numerator and denominator of algebraic fractions to multiply by the same number other than zero, then the value of the fraction will not change. To convert a rational expression in two ways: chain and action. The second method is preferable because it is easier to check the results of the intermediate actions.
Often in expressions it is necessary to extract the roots. The roots of even degree is extracted from only non-negative expressions or numbers. The roots of an odd degree is retrieved from any expressions.