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Examples of mathematical factorization
1、

2^20 1 1 - 2^20 10

= 2^20 10×(2- 1)

= 2^20 10

2、

a^2n - 2a^(2n- 1)

= a^(2n- 1)×(a-2)

3、

( 1-x)+(x- 1)?

= ( x - 1) [ (x- 1)? - 1 ]

=(x- 1)(x? -2x+ 1- 1)

=(x- 1)x(x-2)

=x(x- 1)(x-2)

4、

3^(x+ 1)×2^x-3^x×2^(x+ 1)= 6^6

3×3^x × 2^x - 2×3^x × 2^x = 6^6

3×(3 × 2)^x - 2×(3 × 2)^x = 6^6

(3-2) × 6^x = 6^6

6^x = 6^6

x = 6

5、

x? +ax- 12

Because-12 can be decomposed into (-12)× 1, (-6)×2, (-4)×3, (-3)×4, (-2)×6, (-1).

So the number of a is 6.