Question

Simplify. (Polynomials)

1. (2cd^3)(-2c)(3c^d) =

2. (2x^2)(3x^6) - (4x^4)(2x^4) =

3. (6x^2)(3x^6) + (4x^4)(2x^4) =

4. (2ab^2)^2(-3a^2b^2) =

5. -6a^3(a^2-2a+1) =

6. -2xy(x^2-3xy+y^2) =

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

(Please help asap!)

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))`

`-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)`