note that the coefficients of the last two terms are 6 times the coefficients of the first two
(a - 3b)( a - 6c )
factor by grouping (a^2-3ab)-(6ac+18bc)
then factor out a term from each group that leaves the terms in the parenthesis the same
a(a-3b)-6c(a-3b)
then write the two terms on the outsides as one as well as the two in the parenthesis
(a-6c)(a-3b)
:)
a^2 - 3ab - 6ac + 18bc = (a-3b)(a-6c)
step 1: group
(a^2-3ab) - (6ac-18bc)
step 2: factor
a(a-3b) - 6c(a-3b)
Step 3: combine like terms via the distributive property
a^2 - 3ab - 6ac+18bc
a(a - 3b) - 6c(a - 3b) {factor by grouping}
(a - 6c)(a - 3b)
= a² - 3ab - 6ac + 18bc
= a(a - 3b) - 6c(a - 3b)
= (a - 6c)(a - 3b)
Answer: (a - 6c)(a - 3b)
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Verified answer
note that the coefficients of the last two terms are 6 times the coefficients of the first two
(a - 3b)( a - 6c )
factor by grouping (a^2-3ab)-(6ac+18bc)
then factor out a term from each group that leaves the terms in the parenthesis the same
a(a-3b)-6c(a-3b)
then write the two terms on the outsides as one as well as the two in the parenthesis
(a-6c)(a-3b)
:)
a^2 - 3ab - 6ac + 18bc = (a-3b)(a-6c)
step 1: group
(a^2-3ab) - (6ac-18bc)
step 2: factor
a(a-3b) - 6c(a-3b)
Step 3: combine like terms via the distributive property
(a-6c)(a-3b)
a^2 - 3ab - 6ac+18bc
a(a - 3b) - 6c(a - 3b) {factor by grouping}
(a - 6c)(a - 3b)
= a² - 3ab - 6ac + 18bc
= a(a - 3b) - 6c(a - 3b)
= (a - 6c)(a - 3b)
Answer: (a - 6c)(a - 3b)