What is a simplified in math?

Look up simplification, simplify, or simplified in Wiktionary, the free dictionary.

Simplification, Simplify, or Simplified may refer to:

Mathematics

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler (usually shorter), for example

• Simplification of algebraic expressions, in computer algebra
• Simplification of boolean expressions i.e. logic optimization
• Simplification by conjunction elimination in inference in logic yields a simpler, but generally non-equivalent formula
• Simplification of fractions

Science

• Approximations simplify a more detailed or difficult to use process or model

Linguistics

• Simplification of Chinese characters
• Simplified English (disambiguation)
• Text simplification

Music

• Simplified (band), a 2002 rock band from Charlotte, North Carolina
• Simplified (album), a 2005 album by Simply Red
• "Simplify", a 2008 song by Sanguine
• "Simplify", a 2018 song by Young the Giant from Mirror Master

See also

• Muntzing (simplification of electric circuits)
• Reduction (mathematics)
• Simplicity
• All pages with titles containing Simplification
• All pages with titles containing Simplified
• Oversimplification
  • Dumbing down

Topics referred to by the same term

This disambiguation page lists articles associated with the title Simplification.
If an internal link led you here, you may wish to change the link to point directly to the intended article.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Simplification&oldid=1083188342"

/en/algebra-topics/writing-algebraic-expressions/content/

Simplifying expressions

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression:

4 + 6 + 5

If you simplified it by combining the terms until there was nothing left to do, the expression would look like this:

15

In other words, 15 is the simplest way to write 4 + 6 + 5. Both versions of the expression equal the exact same amount; one is just much shorter.

Simplifying algebraic expressions is the same idea, except you have variables (or letters) in your expression. Basically, you're turning a long expression into something you can easily make sense of. So an expression like this...

(13x + -3x) / 2

...could be simplified like this:

5x

If this seems like a big leap, don't worry! All you need to simplify most expressions is basic arithmetic -- addition, subtraction, multiplication, and division -- and the order of operations.

The order of operations

Like with any problem, you'll need to follow the order of operations when simplifying an algebraic expression. The order of operations is a rule that tells you the correct order for performing calculations. According to the order of operations, you should solve the problem in this order:

1. Parentheses
2. Exponents
3. Multiplication and division
4. Addition and subtraction

Let's look at a problem to see how this works.

In this equation, you'd start by simplifying the part of the expression in parentheses: 24 - 20.

2 ⋅ (24 - 20)2 + 18 / 6 - 30

24 minus 20 is 4. According to the order of operations, next we'll simplify any exponents. There's one exponent in this equation: 42, or four to the second power.

2 ⋅ 42 + 18 / 6 - 30

42 is 16. Next, we need to take care of the multiplication and division. We'll do those from left to right: 2 ⋅ 16 and 18 / 6.

2 ⋅ 16 + 18 / 6 - 30

2 ⋅ 16 is 32, and 18 / 6 is 3. All that's left is the last step in the order of operations: addition and subtraction.

32 + 3 - 30

32 + 3 is 35, and 35 - 30 is 5. Our expression has been simplified—there's nothing left to do.

5

That's all it takes! Remember, you must follow the order of operations when you're performing calculations—otherwise, you may not get the correct answer.

Still a little confused or need more practice? We wrote an entire lesson on the order of operations. You can check it out here.

Adding like variables

To add variables that are the same, you can simply add the coefficients. So 3x + 6x is equal to 9x. Subtraction works the same way, so 5y - 4y = 1y, or just y.

5y - 4y = 1y

You can also multiply and divide variables with coefficients. To multiply variables with coefficients, first multiply the coefficients, then write the variables next to each other. So 3x ⋅ 4y is 12xy.

3x ⋅ 4y = 12xy

The Distributive Property

Sometimes when simplifying expressions, you might see something like this:

3(x+7)-5

Normally with the Order of Operations, we would simplify what is inside the parentheses first. In this case, however, x+7 can't be simplified since we can't add a variable and a number. So what's our first step?

As you might remember, the 3 on the outside of the parentheses means that we need to multiply everything inside the parentheses by 3. There are two things inside the parentheses: x and 7. We'll need to multiply them both by 3.

3(x) + 3(7) - 5

3 · x is 3x and 3 · 7 is 21. We can rewrite the expression as:

3x + 21 - 5

Next, we can simplify the subtraction 21 - 5. 21 - 5 is 16.

3x + 16

Since it's impossible to add variables and numbers, we can't simplify this expression any further. Our answer is 3x + 16. In other words, 3(x+7) - 5 = 3x+16.

/en/algebra-topics/solving-equations/content/

"Like terms" refer to terms whose variables are exactly the same, but may have different coefficients. For example, the terms $2xy$ and $5xy$ are alike as they have the same variable $xy$. The terms $2xy$ and $2x$ are not alike.

Combining like terms refers to adding (or subtracting) like terms together to make just one term.

Since $2xy$ and $5xy$ are like terms (with a variable of $xy$), we can add their coefficients together to get $2xy+5xy=(2+5)xy=7xy$. □ _\square □​

Since $5xy$ and $3xy$ are like terms (with a variable of $xy$), we can subtract their coefficients together to get $5xy-3xy=(5-3)xy=2xy$. □ _\square □​

When there are multiple like terms, arrange the terms in order of decreasing degree and simplify.

Since x2 x^2x2 and 2x2 2x^2 2x2 are like terms (with a variable of x2 x^2x2), we can combine them.
Since $3$ and $7$ are like terms (with a variable of $1$), we can combine them.
The remaining terms are not alike.

Hence, we get x2+3+2x2−4x+7=(1+2)x2−4x+(3+7)=3x2−4x+10. x^2 + 3 + 2x^2 - 4x + 7 = (1+2) x^2 - 4x + (3+7) = 3x^2 - 4x + 10. x2+3+2x2−4x+7=(1+2)x2−4x+(3+7)=3x2−4x+10. The highest degree term is x2 x^2 x2, so the polynomial has degree $2$. □_\square□​

Combining like terms, we get y4+12y−2y3−y4+5y2+52y+3=(y4−y4)−2y3+5y2+3y+3=−2y3+5y2+3y+3. \begin{aligned} y^4 + \frac{1}{2}y - 2y^3 - y^4 + 5y^2 + \frac{5}{2}y + 3 &= \left(y^4 - y^4\right) - 2y^3 + 5y^2 + 3y + 3 \\ &= -2y^3 + 5y^2 + 3y + 3 . \end{aligned} y4+21​y−2y3−y4+5y2+25​y+3​=(y4−y4)−2y3+5y2+3y+3=−2y3+5y2+3y+3.​ The highest degree term is y3 y^3 y3, so the polynomial has degree $3$. □_\square□​

Remember that when adding and subtracting polynomials, the order of operations still applies.

Distributing the minus sign across the terms in the second set of parentheses, we get

2a3−4a2+a−5−2a−2+a3. 2a^3 - 4a^2 + a - 5 - 2a - 2 + a^3. 2a3−4a2+a−5−2a−2+a3.

Collecting similar terms and simplifying, the simplified polynomial is

(2a3+a3)−4a2+(a−2a)−(5+2)=3a3−4a2−a−7. □ \left(2a^3 + a^3\right) - 4a^2 + (a - 2a) - (5 + 2) = 3a^3 - 4a^2 -a -7. \ _\square(2a3+a3)−4a2+(a−2a)−(5+2)=3a3−4a2−a−7. □​

When adding and subtracting polynomials that are in fractional form, start by finding the common denominator of each term.

We have

3a−12−a+24=(3a−12×22)−a+24=(6a−2)−(a+2)4=5a−44. □ \begin{aligned} \frac{3a - 1}{2} - \frac{a + 2}{4} &= \left( \frac{3a - 1}{2} \times \frac{2}{2} \right) - \frac{a + 2}{4} \\ &= \frac{(6a - 2) - (a+2)}{4} \\ &= \frac{5a - 4}{4}. \ _\square \end{aligned} 23a−1​−4a+2​​=(23a−1​×22​)−4a+2​=4(6a−2)−(a+2)​=45a−4​. □​​