The Distributive Property
Example 1: Evaluate:
a) 2(3 +5)
=2(8)
=16
b) 2(3) + 2(5)
=6+10
=16
So 2(3+5)=2(3)+2(5)
ab+c=ab+ac
The Distributive Property:
Allows you to simplify algebraic expressions
Each term inside the brackets is multiplied by the term outside of the brackets
Multiply the coefficients
Use the exponent ruks to multiply the variables.
Example 2: Expand and simplify the following using the distributive property.
a) 5(x + 3)=5(x)+5(3)
=5x+15
b) 2xx2 + 4x-7
=-2xx2-2x4x-2x-7 Use the distribute property
=-21xx2-24xx-2-7x
=-2×1+2-8×1+1+14x
=-2×3-8×2+14x
c) 3y – 7-5y=3y-5y-7-5y Use the distribute prop.
=-15y2+35y multiply double signs
d) -3pp2-7p + 2
=-3pp2-3p-7p-3p2
=-3p1+2+21p1+1-6p
=-3p3+21p2-6p
Example 3: Dmitri simplified the following expression, as shown:
3x(x + 2)
= 3x + 2x
= 5x
a) Explain the errors in Dmitri’s solutions and how to correct them
Dmitri did not use the distributive property
3x(x + 2) = 3x(x) + 3x(2)
=3×2+6x collect solution
b) How can you prove that Dmitri’s answer is not correct?
Substitute x = 1 in the L.
S. (Left Side) and in the R.S. (Right Side) of the equation.
3x(x + 2) = 5x
L.S=3x(x+2)
=3(1)(1+2)
=3(3)
=9
R.S=5(x)
=5(1)
=5
Since the L.SR.S, then Dmitri’s answer is incorrect
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