Simplify the Expression: 2x³·x² - 3x·x⁴ + 6x·x² - 7x³·5

Question

Simplifica la expresión:

2x3x23xx4+6xx27x35= 2x^3\cdot x^2-3x\cdot x^4+6x\cdot x^2-7x^3\cdot 5=

Video Solution

Solution Steps

00:00 Simplify the expression
00:06 When multiplying powers - the power of the result is their sum
00:23 Let's group the factors
00:40 And this is the solution to the question

Step-by-Step Solution

We'll use the law of exponents for multiplication between terms with identical bases:

aman=am+n a^m\cdot a^n=a^{m+n}

We'll apply this law to the expression in the problem:

2x3x23xx4+6xx27x35=2x3+23x1+4+6x1+235x3 2x^3\cdot x^2-3x\cdot x^4+6x\cdot x^2-7x^3\cdot 5=2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3

When we apply the above law to the first three terms from the left, while remembering that any number can always be considered as that number raised to the power of 1:

a=a1 a=a^1

And in the last term we performed the numerical multiplication,

We'll continue and simplify the expression we got in the last step:

2x3+23x1+4+6x1+235x3=2x53x5+6x335x3=x529x3 2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3=2x^5-3x^5+6x^3-35x^3=-x^5-29x^3

Where in the first stage we simplified the expressions in the exponents of the terms in the expression and in the second stage we combined like terms,

Therefore the correct answer is answer A.

Answer

x529x3 -x^5-29x^3