Answer :
We want to multiply the monomial [tex] 2x [/tex] by the monomial [tex] 2x^2 [/tex].
Remember that to multiply monomials we need to use the laws of exponents; in this case, the law for multiplying powers with the same base. The rule says that, when you multiply powers of the same base, you just need to add the exponents: [tex] (a^m)(a^n)=a^{m+n} [/tex], [tex] (x^2)(x^4)=x^{2+4}=x^6 [/tex]. Also, is worth pointing out that the exponent of a variable with no exponent is 1: [tex] x=x^1 [/tex].
Remember that we also need to multiply their coefficients , which are the numbers that multiply the variables; again, variables with no numbers have a coefficient of 1, so [tex] x=1x [/tex]. Multiply coefficients is easy, you just need to multiply them as you usually do with everyday numbers.
Let's apply all of that to our multiplication:
[tex] (2x)(x^2)=(2x^1)(1x^2)=2*1x^{1+2}=2x^3 [/tex]
We can conclude that 2x times x squared is 2x cubed.
[tex]2x[/tex] times [tex]x[/tex] is [tex]\boxed{\bf 2x^{3}}[/tex].
Further explanation:
A monomial is an expression which contains one term and a monomial includes numbers and variables which are multiplied together. The constant term is multiplies with an another constsnt term and the variable is multiplies with an another variable term.
Law of exponent:
Product with same base: If we multiply the same bases with different exponents then the base remains the same and the exponents are added in the final product.
Calculation:
Now, we are given the two monomials as [tex]2x[/tex] and [tex]x^{2}[/tex].
Multiplying both the monomials as follows:
[tex]\boxed{2x\cdot x^{2}}[/tex]
Here, [tex]x[/tex] is a variable and [tex]x[/tex] has power [tex]1[/tex] in the first monomial and [tex]x[/tex] has power [tex]2[/tex] in the second monomial.
Using the mentioned law of exponents as the variable [tex]x[/tex] is similar in both the monomial and add the powers of both as follows:
[tex]\boxed{\begin{aligned}2x\cdot x^{2}&=2x^{1+2}\\&=2x^{3}\end{aligned}}[/tex]
Therefore, [tex]2x[/tex] times [tex]x[/tex] is [tex]\boxed{\bf 2x^{3}}[/tex].
Learn more
1. Problem on the whole numbers are positive integers https://brainly.com/question/1852063.
2. Problem on the adding and simplifying the numbers https://brainly.com/question/894273
3. Problem on general form of the equation of the circle https://brainly.com/question/1506955
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Polynomials
Keywords: Trinomials, binomials, monomials, polynomials, variables, exponents, real numbers, degree of polynomials, equations, expressions, coefficients, zero polynomial, constants, integers, function, domain, range, codomain, graph, abscissa, coordinates, roots of polynomials, bivariate polynomials.
