Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Factorisation - Difference between two squares.
Test Yourself 1.


 

DO NOT FORGET to write each of the terms in brackets as their basic terms squared before starting to factorise!!!

 

Evaluating with numbers
Do not use your calculator but factorise.		 1. 72 - 62
Answer.(7 + 6)(7 - 6) = 13.		 2. 102 - 82
Answer.(10 + 8)(10 - 8) = 36.
  3. 100 - 81
Answer.(10 + 9)(10 - 9) = 18.		 4. 49 - 64
Answer.(7 + 8)(7 - 8) = -15.
Factorising with pronumerals. 5. x2 - 62
Answer.(x + 6)(x - 6).		 6. a2 - 42
Answer.(a + 2)(a - 2).
  7. m2 - n2
Answer.(m + n)(m - n).		 8. p2 - q2
Answer.(p + q)(p - q).
  9. y2 - 9
Answer.(y + 3)(y - 3).		 10. z2 - 25
Answer.(z + 5)(z - 5).
  11. a2 - 144
Answer.(a + 12)(a - 12).		 12. c2 - 49
Answer.(c + 7)(c - 7).
  13. x2 - 1
Answer.(x + 1)(x - 1).		 14. x2 - 2
Answer.(x + √2)(x - √2).
  15. x2 - 16y2
Answer.(x + 4y)(x - 4y).		 16. x4 - y6
Answer.(x2 + y3)(x2 - y3).
  17.
Answer..		 18.
Answer..
  19. 81d2 - 49c4
Answer.(9d + 7c2)(9d - 7c2).		 20.
Answer..
  21. 9x2 - 441
Answer.9(x2 - 49)
= 9(x + 7)(x - 7).		 22. (x + 1)2 - (x - 2)2
Answer.3(2x - 1).
  23. (2x - 3y)2 - 4z2
Answer.(2x - 3y + 2z)(2x - 3y - 2z).		 24. (x + y)2 - (x - y)2
Answer.(2x)(2y)= 4xy.
With factorisation. 25. 27x2y4 - 12z6
Answer.3(9x2y4 - 4z6)
= 3(3xy2 + 2z3)(3xy2 - 2z3).		 26. ae2 - az2
Answer.a(e + z)(e - z).

(so eazy)!!
  27. 20a2 - 45b2
Answer.5(4a2 - 9b2)
= 5(2a + 3b)(2a - 3b).		 28. x4 - 16
Answer.(x2 + 4)(x + 2)(x - 2).
More advanced. 29. sin4x - cos4x
Answer.(sinx - cosx)(sinx + cosx).		 30. Factorise completely:

7x - y + 49x2 - y2

Answer.(7x - y)(1 + 7x +y)).
  31. (3x - 7)2 + 15x - 35
Answer.(3x - 7)(3x - 7 + 5)
=(3x - 7)(3x - 2).		 32. x2 - y2 + 2x +1
Answer.(x + 1 + y)(x + 1 - y).
  33. (2x + 1)2 - 1
Answer.(2x + 2)(2x).		 34. (x + 3)2 - (2x - 5)2
Answer.(3x - 2)(8 - x)).