Factorise :
a+2b+a3+8b3a + 2b + a^3 + 8b^3a+2b+a3+8b3
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(a+2b)+(a3+8b3)=(a+2b)+(a+2b)(a2−2ab+4b2)=(a+2b)[1+(a2−2ab+4b2)]=(a+2b)(1+a2−2ab+4b2)(a + 2b) + (a^3 + 8b^3) = (a + 2b) + (a + 2b)(a^2 - 2ab + 4b^2)\\[1em] = (a + 2b)[1 + (a^2 - 2ab + 4b^2)]\\[1em] = (a + 2b)(1 + a^2 - 2ab + 4b^2)(a+2b)+(a3+8b3)=(a+2b)+(a+2b)(a2−2ab+4b2)=(a+2b)[1+(a2−2ab+4b2)]=(a+2b)(1+a2−2ab+4b2)
Hence, a+2b+a3+8b3=(a+2b)(1+a2−2ab+4b2)a + 2b + a^3 + 8b^3 = (a + 2b)(1 + a^2 - 2ab + 4b^2)a+2b+a3+8b3=(a+2b)(1+a2−2ab+4b2).
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