How do you factor #8a^3 + 27b^3 + 2a + 3b#?

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Answer 1 · 2016-03-29T00:18:26

#8a^3+27b^3+2a+3b=(2a+3b)(4a^2-6ab+9b^2+1)#

From the given expression
#8a^3+27b^3+2a+3b#

#8a^3+27b^3+2a+3b#

#(8a^3+27b^3)+(2a+3b)#

The first two terms can be factored by sum of two cubes formula

#x^3+y^3=(x+y)(x^2-xy+y^2)#

so that #8a^3+27b^3=(2a+3b)(4a^2-6ab+9b^2)#

Let us continue

#(2a+3b)(4a^2-6ab+9b^2)+(2a+3b)#

factor out the common term (2a+3b)

#(2a+3b)(4a^2-6ab+9b^2+1)#

therefore

#8a^3+27b^3+2a+3b=(2a+3b)(4a^2-6ab+9b^2+1)#

God bless...I hope the explanation is useful.