Question

因式分解:(a+b)^3+(a+2b)^3

附上一张图，求解答！！谢谢了。！！

Answer 1

a^3+b^3=(a+b)(a^2-ab+b^2)
原式=（a+b+a+2b）{（a+b）^2-（a+b）（a+2b）+（a+2b）^2}
=（2a+3b）(a^2+3ab+3b^2)

Answer 2

(a + b)^3 + (a + 2b)^3
= [ (a + b) + (a + 2b) ][ (a + b)" - (a + b)(a + 2b) + (a + 2b)" ]
= ( a + b + a + 2b )[ a" + 2ab + b" - ( a" + 3ab + 2b" ) + a" + 4ab + 4b" ]
= ( 2a + 3b )( 2a" + 6ab + 5b" - a" - 3ab - 2b" )
= ( 2a + 3b )( a" + 3ab + 3b" )

Answer 3

(a+b)^3+(a+2b)^3
=(a+b+a+2b)[(a+b)^2-(a+b)(a+2b)+(a+2b^2)]
=(2a+3b)*(a^2+2ab+b^2-a^2-3ab-2b^2+a^2+4ab+4b^2)
=(2a+3b)(a^2+3ab+3b^2)