Chapter 6 FaCtoring and the distributive ProPerty 135

✔SOLUTIONS

1. 3(14 − 2) = 3(14) − 3(2) = 42 − 6 = 36
   2.^1
   2

(6 + 8) =^1

2

(6) +^1

2

(8) = 3 + 4 = 7

3. 4(6 − 2x) = 4(6) − 4(2x) = 24 − 8x


4. 9x(4y + x) = 36xy + 9x^2


5. 3xy^4 (9x + 2y) = 27x^2 y^4 + 6xy^5


6. 3633 xy()–= 21 xx 86 yx–^3 x


7. xx()^1 +=x+=()() ()xx x+=x^2 xx+


8. 10y−3(xy^4 − 8) = 10xy^4 y−3 − 80y−3 = 10xy − 80y−^3


9. 4x^2 (2y − 5x + 6) = 8x^2 y − 20x^3 + 24x^2

Distributing Negative Numbers

Distributing a minus sign or a negative number over addition or subtraction

changes the sign of every term inside the parentheses: –(a + b) = –a – b and

–(a – b) = –a + b. Using the distributive property, we can think of –(a + b) as

(–1)(a + b) and –(a – b) as (–1)(a – b). Therefore,

−(a + b) = (−1)(a + b) = (−1)a + (−1)b = −a + (−b) = −a − b

and

−(a − b) = (−1)(a − b) = (−1)a − (−1)b = −a − (−1)b = −a − (−b) = −a + b.

still struggling

two common mistakes are to write −(a + b) = −a + b and −(a − b) = −a − b.

the minus sign and negative sign in front of the parentheses changes the signs

of every term inside the parentheses, not just the first term.

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