Factoring the Difference of Squares
Intermediate Algebra Skill
Factoring the Difference of Squares
Factor each completely. 1) 9x2 - 1
2) 4n2 - 49
3) 36k2 - 1
4) p2 - 36
5) 2x2 - 18
6) 196n2 - 144
7) 180m2 - 5
8) 294r2 - 150
9) 150k2 - 216
10) 20a2 - 45
11) 3n2 - 75
12) 24x3 - 54x
13) a2 - 25b2
14) 4x2 + 49 y2
15) 25x2 + 16 y2
16) 6a2 + 96b2
17) x2 - 9 y2
18) 49x2 - 25 y2
19) 9x2 - 16 y2
20) 54v2 - 6u2
21) 36a4 - 25b4
22) 2x4r - 72 y4r
23) 125m4 - 20n4
24) 216x4ay - 6 y5a
25) 4x4 - 144 y4
26) 4x4m - 36 y4m
27) 7x4 - 28 y4
28) 7x4 - 343 y4
29) 16m6 - n6
30) 64x6 - y6
Answers to Factoring the Difference of Squares
1) (3x + 1)(3x - 1)
2) (2n + 7)(2n - 7)
3) (6k + 1)(6k - 1)
4) ( p + 6)( p - 6)
5) 2(x + 3)(x - 3)
6) 4(7n + 6)(7n - 6) 7) 5(6m + 1)(6m - 1) 8) 6(7r + 5)(7r - 5)
9) 6(5k + 6)(5k - 6)
10) 5(2a + 3)(2a - 3) 11) 3(n + 5)(n - 5)
12) 6x(2x + 3)(2x - 3)
13) (a + 5b)(a - 5b)
14) Not factorable
15) Not factorable
16) 6(a2 + 16b2)
17) (x + 3y)(x - 3y)
18) (7x + 5y)(7x - 5y)
19) (3x + 4y)(3x - 4y)
20) 6(3v + u)(3v - u)
21) (6a2 + 5b2)(6a2 - 5b2)
22) 2r(x2 + 6 y2)(x2 - 6 y2)
23) 5(5m2 + 2n2)(5m2 - 2n2)
24) 6ay(6x2 + y2)(6x2 - y2)
25) 4(x2 + 6 y2)(x2 - 6 y2)
26) 4m(x2 + 3 y2)(x2 - 3 y2)
27) 7(x2 + 2 y2)(x2 - 2 y2)
28) 7(x2 + 7 y2)(x2 - 7 y2)
29) (4m3 + n3)(4m3 - n3)
30) (2x + y)(2x - y)(4x2 - 2xy + y2)(4x2 + 2xy + y2)
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