Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 153

7. ()()xx–+ 34  =


8. (x − 5)(x + 5) =


9. (x − 6)(x + 6) =


10. ()()xx+–^22 =


11. (x + 8)^2 =


12. (x − y)^2 =


13. (2x + 3y)^2 =


14. ()xy  + ^2 =


15. ()xy +  ()xy–  =

✔SOLUTIONS

1. (5x − 1)(2x + 3) = 5x(2x) + 5x(3) + (−1)(2x) + (−1)(3)
   = 10x^2 + 15x − 2x − 3 = 10x^2 + 13x − 3


2. (4x + 2)(x − 6) = 4x(x) + 4x(−6) + 2x + 2(−6)
   = 4x^2 − 24x + 2x − 12 = 4x^2 − 22x − 12


3. (2x + 1)(9x + 4) = 2x(9x) + 2x(4) + 1(9x) + 1(4)
   = 18x^2 + 8x + 9x + 4 = 18x^2 + 17x + 4


4. (12x − 1)(2x − 5) = 12x(2x) + 12x(−5) + (−1)(2x) + (−1)(−5)
   = 24x^2 − 60x − 2x + 5 = 24x^2 − 62x + 5


5. (x^2 + 2)(x − 1) = x^2 (x) + x^2 (−1) + 2x + 2(−1) = x^3 − x^2 + 2x − 2


6. (x^2 − y)(x + 2y) = x^2 (x) + x^2 (2y) + (−y)x + (−y)(2y)
   = x^3 + 2x^2 y − xy − 2y^2


7. xx xx xx
   x

–  +   ·=  +  + ()–+ ( –)( )

= 

()() 34 4334

( ))^2 +  11 xx–  21 = +  x–  2

8. (x − 5)(x + 5) = x(x) + 5x + (−5)x + (−5)(5)
   = x^2 + 5x − 5x − 25 = x^2 − 25


9. (x − 6)(x + 6) = x(x) + 6x + (−6)x + (−6)(6)
   = x^2 + 6x − 6x − 36 = x^2 − 36


10. xx xx xx
    x

+  –  =  + ()–+  + –()

= 

()() 22 ()() 2222

(()

2

–  22 xx +  –  44   = x–