The sum of cubez!! plz help!! will give 10 points!! Thankz!!!?

Question

The Sum and Difference of Cubes

The ^ stands for exponente

Please complete the following exercises

1.) 64^3+1

2.) 1-125b^3

3.) 8x^3y^6+27

4.) a^3b^6-b^3 (Remember to take out the GCF)

5.) 27x^3-8y^3

Answer 1

the formulae  for solvin' the following problems are:

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

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

1.) 64^3+1

(64+1){64^2+1^2-64*1}

=65(4033)

=262145

2.) 1-125b^3

=1-(5b)^3

(1-5b)(1+25b^2+5)

3.) 8x^3y^6+27

=(2xy^2)^3+3^3

=(2xy^2+3){(2xy^2)^2+3^2-2xy^2*3}

=(2xy^2+3){4x^2y^4+9-6xy^2}

4.) a^3b^6-b^3

b^3(a^3-1)

=b^3(a-1)(a^2+1-a)

5.) 27x^3-8y^3

(3x)^3-(2y)^3

=(3x-2y)(9x^2+4y^2+6xy)

Please rate me ::))

Answer 2

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

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

1)

64^3 + 1

= 64^3 + 1^3

= (64 + 1)(64^2 - 64 + 1^2)

= (65)(4096 - 64 + 1)

= (65)(4033)

= 262145

2)

1 - 125b^3

= 1^3 - 125b^3

= (1 - 5b)(1 + 5b + 25b^2)

3)

8x^3y^6 + 27

= 2^3x^3(y^2)^3 + 3^3

= (2xy^2 + 3)(4x^2y^4 - 6xy^2 + 9)

4)

a^3b^6 - b^3

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

= b(ab - 1)(a^2b^4 + ab^3 + b^2)

= b^3(ab - 1)(a^2b^2 + ab + 1)

5)

27x^3 - 8y^3

= (3x - 2y)(9x^2 + 6xy + 4y^2)

Answer 3

Sum of Cubes:

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

Difference of Cubes:

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

1)

64^3 + 1

= 64^3 + 1^3

= (64 + 1)(64^2 - (64)(1) + 1^2)

= (65)(4096 - 64 + 1)

= (65)(4033)

= 262145

2)

1 - 125b^3

= 1^3 - 5^3 b^3

= 1^3 - (5b)^3

= (1 - 5b)(1^2 + 1(5b) + (5b)^2)

= (1 - 5b)(1 + 5b + 25^2)

3)

8x^3y^6 + 27

= 2^3 x^3 y^6 + 3^3

= (2xy^2)^3 + 3^3

= (2xy^2 + 3)[(2xy^2)^2 - (2xy^2)(3) + 3^2]

= (2xy^2 + 3)(4x^2y^4 - 6xy^2 + 9)

4)

a^3b^6 - b^3

= (b^3)(a^3 b^3 - 1)

= (b^3)[(ab)^3 - 1^3]

= (b^3)(ab - 1)(a^2b^2 + ab + 1)

5)

27x^3 - 8y^3

= (3x)^3 - (2y)^3

I think you can finish this one yourself now.

Answer 4

1) (64 + 1)(64^2 - 64 + 1) = 65 x (4096 - 64 +1)

2) (1 - 5)(1 + 5 + 5^2)= (-4)x31 = -124

3) (2xy^2+3)(4x^2y^4 - 6xy^2 + 9)

4) b^3(a^3b^3-1) = b^3(ab-1)(a^2b^2+ab+1)

5) (3x-2y)(9x^2 + 6xy + 4y^2)