Algebra 1 Help

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Algebra 1 helps us to convert a big word problem into a simple expression or equation by using signs and symbols.
 

Algebraic expressions: - An algebraic expression is a collection of one or more terms, which are separated from each other by he signs + (plus), – (minus), x (multiply) or /and / (divide).
 

 
Expressions Number of terms used Terms
7 x + 3 x y + 2 y 3 7x, 3xy, 2y
2 x + 5 x y 2 2 x, 5 x y
4 x – 6 y + 7 3 4 x, 6 y, 7
7 x y + 2 a / y – 3 z + 8 4 7 x y, 2 a / y, 3 z, 8
 

In algebraic expression 4 x – y + 7; 7 is the constant term as it does not contain any variable. Similarly in algebraic expression 7 x y + 2 a / y – 3 z + 8; 8 is the constant term.
 

Example 1: - Find the value of the following expression when x = -1
            x^3 +x^2 + x +1
 

Solution: -Substitute the value x = -1 in the given expression
            x^3 +x^2 + x +1 = (- 1)^3 + (- 1)^2 + (- 1) + 1
                                         = - 1 + 1 – 1 + 1
                                         = -2 + 2
                                         = 0
 

Example 2: -Factorize the same above expression
 

Solution: - x^3 +x^2 + x +1 = x^2 (x + 1) + 1 (x + 1)
                                               = (x + 1) (x^2 + 1)



 

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