How do you multiply and simplify #\frac { a ^ { 2} - b ^ { 2} } { a + 2b } \cdot \frac { a ^ { 2} - a } { ( b - a ) }#?

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Answer 1 · 2017-06-06T14:05:40

See explanation

Note that #a^2-b^2# is the same as #(a+b)(a-b)# giving:

#((a+b)(a-b))/(a+2b)xx(a(a-1))/(b-a)#

Note that #b-a# is the same as #-(a-b)# giving

#((a+b)(a-b))/(a+2b)xx[-(a(a-1))/(a-b)]#

#((a+b)cancel((a-b)))/(a+2b)xx[-(a(a-1))/(cancel((a-b)))]#

#-(a(a-1)(a+b))/(a+2b)" " larr" Choice 1"#

#-(a(a^2+ab-a-b))/(a+2b)" " larr" Choice 2"#

#-(a^3+a^2b-a^2-ab)/(a+2b)" "larr" Choice 3"#