[20] Factorization

1. (3u^2 - v)(3u^2 + v)
= (3u^2)^2 - v^2
= 9u^4 - v^2

2. (rs + t^2)(rs - t^2)
= (rs)^2 - (t^2)^2
= r^2s^2 - t^4

3. (-ax - by)(by - ax)
= -(by + ax)(by - ax)
= - [(by)^2 - (ax)^2]
= - (b^2y^2 - a^2x^2)
= a^2x^2 - b^2y^2

4. -0.5(-2y-0.5x)(-0.5x+2y)
= 0.5(2y + 0.5x)(2y - 0.5x)
= 0.5[(2y)^2 - (0.5x)^2]
= 0.5(4y^2 - 0.25x^2)
= 2y^2 - 0.125x^2

5. (x+a)(x+a)(x^2 + a^2)
= (x^2 + 2ax + a^2)(x^2 + a^2)
= x^4 + a^2x^2 + 2ax^3 + 2a^3x + a^2x^2 + a^4
= x^4 + 2a^2x^2 + 2ax^3 + 2a^3x + a^4

6. 16m^2 n^2 - (-3)^2
= (4mn)^2 - (-3)^2
= [(4mn + (- 3)][(4mn - (-3)]
= (4mn - 3)(4mn + 3)

7. 2x^3 - 18x
= 2x(x^2 - 9)
= 2x[(x)^2 - 3^2]
= 2x(x - 3)(x + 3)

8. a^2 b^3 - 25a^2 b
= b(a^2 b^2 - 25a^2)
= b[(ab)^2 - (5a)^2]
= b(ab + 5a)(ab - 5a)

9. 50kmx^2 - 2km^3
= 2km(25x^2 - m^2)
= 2km[(5x)^2 - m^2]
= 2km(5x + m)(5x - m)

10. 16(x+2y)^2 - 36(x-y)^2
= [4(x + 2y)]^2 - [8(x - y)]^2
= [4(x + 2y) + 8(x - y)][4(x + 2y) - 8(x - y)]
= (4x + 8y + 8x - 8y)(4x + 8y - 8x + 8y)
= (12x)(-4x + 16y)
= 48x(4y - x)

11. (a+b-c)^2 - (a-b+c)^2
= [(a + b - c) + (a - b + c)][(a + b - c) - (a - b + c)]
= (a + b - c + a - b + c)(a + b - c - a + b - c)
= (2a)(2b - 2c)
= 4a(b - c)

12. x^2 / 9 - y^2 / 25
= (x / 3)^2 - (y / 5)^2
= (x / 3 + y / 5)(x / 3 - y / 5)

13. 0.25h^2 - 0.16k^2
= (0.5h)^2 - (0.4k)^2
= (0.5h + 0.4k)(0.5h - 0.4k)

EXPAND:1. 9u^4-v2 2.r^2s^2-t^4 3. -a^2x^2+b^2y^2 4. 0.125+2y^2
5. 2x^3a+x^2+a^2+2xa^3
FACTORIZATION:6.(4mn+3)(4mn-3) 7. 2x(x+3)(x-3) 8. a^2b(b+5)(b-5) 9. 2km(5x+m)(5x-m) 10. 4[2(x+2y)-3(x-y)][2(x+2y)+3(x-y)]