Difference of squares — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
a2 - b2 = (a - b)(a + b).
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
Practise this idea
6 questions in the course bank use Difference of squares, in Expressions, Structure & Units, Polynomial Operations, Factoring, Radicals & Rational Exponents.
Problem 1
Factor x4 - 16 completely.
Worked answer
(x - 2)(x + 2)(x^2 + 4)
(x2)2 - 42 = (x2 - 4)(x2 + 4)
x2 - 4 = (x-2)(x+2)
x2 + 4 does not factor
Problem 2
Expand (3x - 2)(3x + 2).
Worked answer
9x^2 - 4
9x2
6x - 6x = 0
-4
A difference of squares
Problem 3
Factor x2 - 36.
Worked answer
(x - 6)(x + 6)
x2 - 62
(x - 6)(x + 6)
Problem 4
Factor 3x3 - 27x completely.
Worked answer
3x(x - 3)(x + 3)
3x(x2 - 9)
3x(x - 3)(x + 3)
Problem 5
Factor x4 - 81 completely.
Worked answer
(x - 3)(x + 3)(x^2 + 9)
(x2 - 9)(x2 + 9)
(x-3)(x+3)(x2+9)
Problem 6
Expand (√3 + 2)(√3 - 2).
Worked answer
-1
(√3)2 - 22
= 3 - 4 = -1
A rational answer from irrational parts