[tex]$5 x^2-2\left(x-3 x^2\right)$[/tex]
Answer (2)
The expression 5 x 2 − 2 ( x − 3 x 2 ) simplifies to 11 x 2 − 2 x by distributing and combining like terms. First, we distribute the -2, and then we combine the resulting terms. The final simplified expression is 11 x 2 − 2 x .
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Distribute the -2: − 2 ( x − 3 x 2 ) = − 2 x + 6 x 2 .
Combine the result with the first term: 5 x 2 − 2 x + 6 x 2 .
Combine like terms: ( 5 x 2 + 6 x 2 ) − 2 x = 11 x 2 − 2 x .
The simplified expression is 11 x 2 − 2 x .
Explanation
Understanding the Problem We are given the expression 5 x 2 − 2 ( x − 3 x 2 ) and our goal is to simplify it. This involves distributing the − 2 across the terms inside the parenthesis and then combining like terms to arrive at a simplified expression.
Distributing the -2 First, we distribute the − 2 into the parenthesis: − 2 ( x − 3 x 2 ) = − 2 x + 6 x 2
Combining with the First Term Now, we combine this result with the first term in the original expression: 5 x 2 − 2 x + 6 x 2
Combining Like Terms Next, we combine like terms. The terms 5 x 2 and 6 x 2 are like terms, so we can add them together: ( 5 x 2 + 6 x 2 ) − 2 x = 11 x 2 − 2 x
Final Answer Therefore, the simplified expression is 11 x 2 − 2 x .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with applications in various fields. For example, in physics, you might need to simplify an expression representing the kinetic energy of an object. If the kinetic energy K E is given by K E = f r a c 1 2 m v 2 − f r a c 1 2 m ( 2 v ) 2 , where m is mass and v is velocity, simplifying this expression would give you K E = − f r a c 3 2 m v 2 , allowing for easier calculations and a better understanding of the relationship between mass, velocity, and kinetic energy.
