Algebraic Expression

The algebraic expressions have the variables and the constants. The algebraic expressions are the finite combination of the symbols that are formed according to the rules of the context. The algebra is an expression which is used to designate the value for the given values in the expression. The expression might be depending on the values assigned to the values assigned in the expression. The expression is the syntactic concept in the algebra. The online provides the connectivity between the tutors and the students. This article has the information about learn online algebraic expressions.

Below are the examples on Simplifying algebraic expressions

Example 1

Compute the factors for the expression x²+ 56x+ 768.

Solution:

The given expression is x²+ 56x+ 768.

Step 1: x²+ 56x+ 768 = x²+24x+ 32x+ (24x 32)
Step 2: x²+ 56x+ 768 = x(x+24) + 32(x +24)
Step 3: x²+ 56x+ 768 = (x+24) (x+32)
Step 4: x+24 and x+32

The factors for the given expression x²+ 56x+ 768 are (x +24) and (x +32).

Example 2

Compute the factors for the expression x²+ 76x+ 1440.

Solution:

The given expression is x²+ 76x+ 1440.

Step 1: x²+ 76x+ 1440 = x²+36x+ 40x+ (36x 40)
Step 2: x²+ 76x+ 1440 = x(x+36) + 40(x +36)
Step 3: x²+ 76x+ 1440 = (x+36) (x+40)
Step 4: x+36 and x+40

The factors for the given expression x²+ 76x+ 1440 are (x +36) and (x +40).

Example 3

Simplify the expression 24xy + 10 x²y + 14 x y + 16 x²y + 10 x y.

Solution:

The given expression is 24xy + 10 x²y + 14 x y + 16 x²y + 10 x y.

Step 1: 24xy + 10 x²y + 14 x y + 16 x²y + 10 x y = x y (24 +14 +10) + x²y (10+ 16)
Step 2: 24xy + 10 x²y + 14 x y + 16 x²y + 10 x y = 48 x y + x²y (10+ 16)
Step 3: 24xy + 10 x²y + 14 x y + 16 x²y + 10 x y = 48 x y + 26 x²y

The value for the given expression 12xy + 13 x²y + 16 x y + 20 x²y is 48 x y + 26 x²y.

Below are the practice problems on algebraic expressions-

• Determine the value for the algebraic expression x²+ 50x+ 600.

Answer: (x + 30) (x + 20)

• Simplify the expression 80 x y + 15 x²y + 5 x y + 17 x²y.

Answer: 85 x y + 32 x²y.