How do you factor 8(5x + 7)^3 + 27(x-9)^3?

1 Answer
Dec 31, 2015

Use the sum of cubes identity to find:

8(5x+7)^3 + 27(x-9)^3 = 13(x-1)(79x^2+346x+1303)

Explanation:

The sum of cubes identity may be written:

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

Use this with a=10x+14 and b=3x-27 as follows...

8(5x+7)^3 + 27(x-9)^3

= 2^3(5x+7)^3 + 3^3(x-9)^3

= (10x+14)^3+(3x-27)^3

= ((10x+14)+(3x-27))((10x+14)^2-(10x+14)(3x-27)+(3x-27)^2)

= (13x-13)((100x^2+280x+196)-(30x^2-228x-378)+(9x^2-162x+729))

=13(x-1)(79x^2+346x+1303)