Problems

1. Factor the following expression.

   (a) $18u^2x^6-3u^9x^5y^3 $

   (b) $12vw^2y^9+20v^3w^8$

2. Factor

   (a) $5u^2(u+8)+3(u+8)$

   (b) $8w(w+6)+(w+6)$

3. Factor by grouping.

   (a). $5v^3-6v^2-35v+42$

   (b). $2x^5+x^4+12x+6$

4. Factor by grouping.

   (a) $4u^2+6w-24u-uw$

   (b) $2y-7w^2-wy+14w$

5. Factor. (difference of squares)

   (a). $81x^2-64$

   (b). $4-9y^2$

   (c). $w^2v^2-81$

6. Factor. (sum or difference of cubes)

   (a) $8x^3+27$

   (b) $y^3-125$

Answer key

1. (a) $3u^2x^5(6x-u^7y^3)$

   (b) $4vw^2(3y^9+5v^2w^6)$

2. (a) $(u+8)(5u^2+3)$

   (b) $(w+6)(8w+1)$

3. (a) $(5v-6)(v^2-7)$

   (b) $(2x+1)(x^4+6)$

4. (a) $(u-6)(4u-w)$

   (b) $(2-w)(y+7w)$

5. (a) $(9x+8)(9x-8)$

   (b) $(2+3y)(2-3y)$

   (c) $(wv+9)(wv-9)$

6. (a). $(2x+3)(4x^2-6x+9)$

   (b). $(y-5)(y^2+5y+25)$