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
#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)#
