134 algebra De mystif ieD
The distributive property of multiplication over addition, a(b + c) = ab + ac,
says that we can first take the sum (b + c) and then the product (a times the
sum of b and c) or the individual products (ab and ac) and then the sum (the
sum of ab and ac). For instance, 12(6 + 4) could be computed as 12(6 + 4) =
12(6) + 12(4) = 72 + 48 = 120 or as 12(6 + 4) = 12(10) = 120. The distributive
property of multiplication over subtraction, a(b – c) = ab – ac, says the same
about a product and difference. Rather than working with numbers, we will use
the distributive property to work with algebraic expressions. We begin with
simple variables.EXAMPLES
Use the distributive property to rewrite the expression.
In distributing variables, we often use the exponent property aamn=amn+.7(x – y) = 7x – 7y 4(3x + 1) = 12x + 4
x^2 (3x – 5y) = 3x^3 – 5x^2 y 8 xy(x^3 + 4y) = 8x^4 y + 32xy^2
6 x^2 y^3 (5x – 2y^2 ) = 30x^3 y^3 – 12x^2 y^5 xx()^22 += 12 xx+ 12 x
y –2 (y^4 + 6) = y –2 y^4 + 6y–2 = y^2 + 6y–2 32 xy()xy^23 +– 57 =+ 61 xy 52 xy^2 – 1 xyPRACTICE
Use the distributive property to rewrite the expression.- 3(14 − 2) =
2.^1
2
() 68 +=- 4(6 − 2x) =
- 9x(4y + x) =
- 3xy^4 (9x^3 + 2y) =
- 363 xy()–= 2 x
- xx()1+ =
- 10y−3(xy^4 − 8) =
- 4x^2 (2y − 5x + 6) =
EXAMPLES
Use the distributive property to rewrite the expression.PRACTICE
Use the distributive property to rewrite the expression.