To simplify an expression means to replace it by an equal one that is shorter or easier to compute.
The main tool in this lesson is the distributive property of multiplication over addition:
a⋅(b+c)=a⋅b+a⋅c.
The reverse form is also true (factoring out a common factor):
a⋅b+a⋅c=a⋅(b+c).
Simplifying does not change the value of the expression; it only makes calculation easier: fewer intermediate steps, easier mental math and column work.
a(b+c)=ab+ac
ab+ac=a(b+c)
Simplifying preserves the value
Pick the form that is faster to evaluate
Distributive property: expand parentheses
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