[20] Factorization

1. 0.04(x-2y)^2 - 0.25y^2
= [0.2(x - 2y)]^2 - (0.5y)^2
= [0.2(x - 2y) + 0.5y][0.2(x - 2y) - 0.5y]
= (0.2x - 0.4y + 0.5y)(0.2x - 0.4y - 0.5y)
= (0.2x + 0.1y)(0.2x - 0.9y)

2. 4(x+y+z)^2 - (2x-3y-4z)^2
= [2(x+y+z)]^2 - (2x - 3y - 4z)^2
= [2(x + y + z) + (2x - 3y - 4z)][(2(x + y + z) - (2x - 3y - 4z)]
= (2x + 2y + 2z + 2x - 3y - 4z)(2x + 2y + 2z - 2x + 3y + 4z)
= (4x - y - 2z)(5y + 6z)

3. m^4 - 16
= (m^2)^2 - 4^2
= (m^2 + 4)(m^2 - 4)
= (m^2 + 4)(m + 2)(m - 2)

4. bw^5 - b^5 w
=bw (w^4 - b^4)
= bw[(w^2)^2 - (b^2)^2]
=bw(w^2 + b^2)(w^2 - b^2)
=bw(w^2 + b^2)(w + b)(w - b)

5. (0.05x - 2)^2
= 0.0025x^2 - 0.2x + 4

6. (4m+0.5n)^2
= 16m^2 + 4m + 0.25n^2

7. (a/2 - b/3)^2
= a^2 / 4 - (ab) / 3 + b^2 / 9

8. (a/2 - 1/a)^2
= a^2 / 4 - 1 + 1 / a^2

9. (-5h^2 - k^2 )^2
= (-5h^2)^2 - 2(-5h^2)(k^2) + (k^2)^2
= 25h^4 + 10h^2k^2 + k^4

10. (2y^2 - 5x^2 y)^2
= (2y^2)^2 - 2(2y^2)(5x^2y) + (5x^2y)^2
= 4y^4 - 20x^2 y^3 + 25x^4 y^2

11. (2k+u)^2
= 4k^2 + 4ku + u^2

12. (2k+x-y)^2
= [(2k + x) - y]^2
= (2k + x)^2 - 2(2k + x)(y) + y^2
= 4k^2 + 2kx + x^2 - 4ky - 2xy + y^2