Do the Factorise
(x+3)^8 in X^5
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The sum of cubes identity may be written:
a3+b3=(a+b)(a2−ab+b2)
We use this with a=x and b=2 to find:
x5+x3+8x2+8
=(x5+x3)+(8x2+8)
=(x2+1)x3+(x2+1)8
=(x2+1)(x3+8)
=(x2+1)(x3+23)
=(x2+1)(x+2)(x2−x(2)+22)
=(x2+1)(x+2)(x2−2x+4)
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