My question is to please help me with factoring completly. here some that i need help on just three? 1. x^3-8 2. 27^6+125y^3 3. x^3-2x^2-4x+8
I don't really understand much especially gcf and stuff like factoring completely please help,
I don't really understand much especially gcf and stuff like factoring completely please help,
1 Answer
1)
2)
27x^6+125y^3 = (3x^2+5y)(9x^4-15x^2y+25y^2)
3)
Explanation:
The difference of cubes identity can be written:
a^3-b^3=(a-b)(a^2+ab+b^2)
The sum of cubes identity can be written:
a^3+b^3=(a+b)(a^2-ab+b^2)
The difference of squares identity can be written:
a^2-b^2=(a-b)(a+b)
Question 1
Use the difference of cubes identity with
x^3-8
=x^3-2^3
=(x-2)(x^2+2x+2^2)
=(x-2)(x^2+2x+4)
Question 2
Use the sum of cubes identity with
27^6+125y^3
=(27^2)^3+(5y)^3
=(729+5y)(729^2-729*5y+(5y)^2)
=(729+5y)(531441-3645y+25y^2)
Actually I suspect a typo in the question. If
27x^6+125y^3
=(3x^2)^3+(5y)^3
=(3x^2+5y)((3x^2)^2-(3x^2)(5y)+(5y)^2)
=(3x^2+5y)(9x^4-15x^2y+25y^2)
Question 3
Factor by grouping:
x^3-2x^2-4x+8
=(x^3-2x^2)-(4x-8)
=x^2(x-2)-4(x-2)
=(x^2-4)(x-2)
=(x^2-2^2)(x-2)
=(x-2)(x+2)(x-2)
