Question

Simplify. (Polynomials)

Answer 1

1.$(2cd^{3})(-2c)(3cd)$
   $-12c^{3}d^{4}$

2.$(2x^{2})(3x^{6}) - (4x^{4})(2x^{4})$
   $6x^{8} - 8x^{8}$
   $-2x^{8}$

3.$(6x^{2})(3x^{6}) + (4x^{4})(2x^{4})$
   $18x^{8} + 8x^{8}$
   $26x^{8}$

4.$(2ab^{2})^{2}(-3a^{2}b^{2})$
   $((2ab^{2})(2ab^{2}))(-3a^{2}b^{2})$
   $(4a^{2}b^{4})(-3a^{2}b^{2})$
   <u />$-12a^{4}b^{6}$

5.$-6a^{3}(a^{2} - 2a + 1)$
   $-6a^{3}(a^{2}) + 6a^{3}(2a) - 6a^{3}(1)$
   $-6a^{5} + 12a^{4} - 6a^{3}$

6.$-2xy(x^{2} - 3xy + y^{2})$
   $-2xy(x^{2}) + 2xy(3xy) - 2xy(y^{2})$
   $-2x^{3}y + 6x^{2}y^{2} - 2xy^{3}$

7.$(a + b)(2a^{2} - ab + 3b^{2})$
   $(2a^{3} - a^{2}b + 3ab^{2} + 2a^{2}b - ab^{2} + 3b^{3})$
   $(2a^{3} - a^{2}b + 2a^{2}b + 3ab^{2} - ab^{2} + 3b^{3})$
   $2a^{3} + a^{2}b + 2ab^{2} + 3b^{3}$
  

Answer 2

1. $(2cd^{3})(-2c)(3c^{d})=\\-12c^{d+2}d^{3}$

2. $(2x^{2})(3x^{6})-(4x^{4})(2x^{4})=\\6x^{8}-8x^{8}=\\-2x^{8}$

3. $(6x^{2})(3x^{6})+(4x^{4})(2x^{4})=\\18^{8}+8x^{8}=\\26x^{8}$

4. $(2ab^{2})^{2}(-3a^{2b^{2}})=\\4a^{2}b^{4}(-3a^{2b^{2}})=\\-12a^{2b^{2}+2}b^{4}$

5. $-6a^{3}(a^{2}-2a+1)=\\-6a^{5}+12a^{4}-6a^{3}$

6. $-2xy(x^{2}-3xy+y^{2})=\\-2x^{3}y+6x^{2}y^{2}-2xy^{3}$

7. $(a+b)(2a^{2}-ab+3b^{2})=\\2a^{3}-a^{2}b+3ab^{2}+2a^{2}b-ab^{2}+3b^{3}=\\2a^{3}+3b^{3}+a^{2}b+2ab^{2}$