Identities simplify expression

In summary, simplifying an expression involves rewriting it in a simpler form without changing its value. Identities in mathematics are equations that are always true, and they can be used to simplify expressions and solve equations. Basic identity rules in algebra include the commutative, associative, and distributive properties. An expression is fully simplified when it cannot be simplified any further using basic algebra rules. Some tips for simplifying expressions include identifying like terms, using basic identity rules, and following the order of operations. It is also helpful to work from the inside out and double check your work by plugging in values for the variables.
  • #1
I have been trying to do this problem for a long time, and still can not do it. I know the answer is sin2x, but I have no idea how to do it:

write expression as sine, cosine, or tangent of an angle

sin3xcosx - cos3xsinx

THANKS!
 
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  • #2
Use the sine addition formula, sin(a-b)=sin(a)cos(b)-cos(a)sin(b). Line that up with your expression and figure out what a and b should be.
 

What does it mean to simplify an expression?

Simplifying an expression means to rewrite it in a simpler form without changing its value. This is often done by combining like terms or using mathematical rules to reduce the number of terms in the expression.

What are identities in mathematics?

In mathematics, identities are equations or expressions that are always true, regardless of the value of the variables involved. These can be used to simplify expressions and solve equations.

What are the basic identity rules in algebra?

Some basic identity rules in algebra include the commutative property, associative property, and distributive property. The commutative property states that the order of the terms in an expression can be changed without changing its value. The associative property states that the grouping of terms in an expression can be changed without changing its value. The distributive property states that multiplying a number or variable by a sum or difference is the same as multiplying it by each term separately and then adding or subtracting the products.

How do I know if an expression is fully simplified?

An expression is fully simplified when it cannot be simplified any further using the basic rules of algebra. This means that all like terms have been combined, parentheses have been removed, and the terms are in their simplest form.

What are some tips for simplifying expressions?

Some tips for simplifying expressions include identifying like terms, using the basic identity rules, and remembering the order of operations. It can also be helpful to work from the inside out, simplifying terms within parentheses first, and to double check your work by plugging in values for the variables to see if the original and simplified expressions have the same value.

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