Pre algebra monomials
Introduction :
Pre algebra is the sub-division of algebra. Pre algebra is a study in school levels. Pre algebra is used to study about basic of algebra. The topics of Pre algebra are numbers, integers, fractions, decimals, percent, square roots, expressions and equations, ratio and proportion, geometry, graphing, Polynomials and monomials.
In this article, we will study about monomials in pre algebra.
Pre algebra : Monomials:
Algebraic expression includes variables and numbers, arithmetic operation symbols, grouping symbols. Addition, subtraction, multiplication, division are basic arithmetic operations.
A monomial is said to be an algebraic expression which has only one term in the expression. For example, 5x2, -10y, 4x3y3.
Monomial comes under polynomials. In other words, it is one type of polynomials. Polynomial is said to be an algebraic expression which has one term or more than one term.
Let us see different sample problems on monomials.
Example solved Problems:
Problem 1:
What is the prime factorization of this monomial? 25n2.
Solution:
25n2 = 5 x 5 x n x n
Problem 2:
What is the prime factorization of this monomial? 36x3.
Solution:
36x3 = 6 · 6 · x · x · x
Problem 3:
What is the prime factorizations of this monomial? 84ab.
Solution:
84ab = 2 x 2 x 3 x 7 x a x b = 22 x 3 x 7 x a x b
Problem 4:
Find the sum of two monomials: 15x2y and -10yx2
Solution:
Addition of monomials: 15x2y + (-10yx2) = 15x2y – 10yx2
= 5 x2y .
Problem 5:
Find the sum of two monomials: -25z3 and 55z3
Solution:
Addition of monomials: -25z3 + 55z3 = 55z3 – 25z3
= 30z3 .
Problem 6:
Multiply the monomials. 9xy and 5xy.
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
9xy · 5xy = (9·5) · (x·x) · (y·y)
= 45x2·y2
Problem 7:
Multiply the monomials. -8a2 and 2a3b2.
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
-8a2 · 2a3b2 = (-8·2) · (a2·a3) · (b2)
= -16 a5 b2
Problem 8:
Multiply the monomials. 7xy and 3x2z and -2yxz2
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
7xy · 3x2z · -2yxz2 = (7·3·-2) · (x·x2·x) · (y·y) · (z·z2)
= -42 x4 y2 z3
Problem 9:
Divide by 16x4 by 4x3 monomials.
Solution
If a variable is divided by another variable with the same exponent, the exponent of the variable denominator is reduced(subtracted) from the exponent of the variable in the numerator.
16x4 ÷ 4x3 = `(16x^4)/(4x^3) `
= 4 x4-3 = 4 x1 = 4x .
Pre algebra is the sub-division of algebra. Pre algebra is a study in school levels. Pre algebra is used to study about basic of algebra. The topics of Pre algebra are numbers, integers, fractions, decimals, percent, square roots, expressions and equations, ratio and proportion, geometry, graphing, Polynomials and monomials.
In this article, we will study about monomials in pre algebra.
Pre algebra : Monomials:
Algebraic expression includes variables and numbers, arithmetic operation symbols, grouping symbols. Addition, subtraction, multiplication, division are basic arithmetic operations.
A monomial is said to be an algebraic expression which has only one term in the expression. For example, 5x2, -10y, 4x3y3.
Monomial comes under polynomials. In other words, it is one type of polynomials. Polynomial is said to be an algebraic expression which has one term or more than one term.
Let us see different sample problems on monomials.
Example solved Problems:
Problem 1:
What is the prime factorization of this monomial? 25n2.
Solution:
25n2 = 5 x 5 x n x n
Problem 2:
What is the prime factorization of this monomial? 36x3.
Solution:
36x3 = 6 · 6 · x · x · x
Problem 3:
What is the prime factorizations of this monomial? 84ab.
Solution:
84ab = 2 x 2 x 3 x 7 x a x b = 22 x 3 x 7 x a x b
Problem 4:
Find the sum of two monomials: 15x2y and -10yx2
Solution:
Addition of monomials: 15x2y + (-10yx2) = 15x2y – 10yx2
= 5 x2y .
Problem 5:
Find the sum of two monomials: -25z3 and 55z3
Solution:
Addition of monomials: -25z3 + 55z3 = 55z3 – 25z3
= 30z3 .
Problem 6:
Multiply the monomials. 9xy and 5xy.
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
9xy · 5xy = (9·5) · (x·x) · (y·y)
= 45x2·y2
Problem 7:
Multiply the monomials. -8a2 and 2a3b2.
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
-8a2 · 2a3b2 = (-8·2) · (a2·a3) · (b2)
= -16 a5 b2
Problem 8:
Multiply the monomials. 7xy and 3x2z and -2yxz2
Solution:
To multiply the two monomials, there are two steps. First multiply the constants and add the exponents of the same variables.
7xy · 3x2z · -2yxz2 = (7·3·-2) · (x·x2·x) · (y·y) · (z·z2)
= -42 x4 y2 z3
Problem 9:
Divide by 16x4 by 4x3 monomials.
Solution
If a variable is divided by another variable with the same exponent, the exponent of the variable denominator is reduced(subtracted) from the exponent of the variable in the numerator.
16x4 ÷ 4x3 = `(16x^4)/(4x^3) `
= 4 x4-3 = 4 x1 = 4x .