How do you factor #2( a+b) ^2 + (a+b) - 21#?
1 Answer
Mar 2, 2018
Explanation:
#"make the substitution "u=a+b" then"#
#2u^2+u-21larrcolor(blue)"is the expression to be factored"#
#"the product of - 42 which sums to + 1 is + 7 and - 6"#
#rArr2u^2-6u+7u-21#
#=color(red)(2u)(u-3)color(red)(+7)(u-3)#
#=(u-3)(color(red)(2u+7))#
#"changing u back to a + b"#
#=(a+b-3)(2a+2b+7)#
#rArr2(a+b)^2+(a+b)-21#
#=(a+b-3)(2a+2b+7)#
