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(A).
\The expression is 54y + 6.
\First find the GCF of 54y and 6.
\Factor the each monomial and Circle the common prime factors.
\
The product of the common prime factors, 2 · 3 or 6, is called the greatest common factor of 54y and 6.
\Write each term as the product of the GCF and its remaining factors.Then use the Distributive Property to factor out the GCF.
\54y + 6 = 6(3 · 3 · y) + 6(1)
\= 6(9y) + 6(1)
\= 6(9y + 1).
\The completely factored form of 54y + 6 is 6(9y + 1).
\(B).
\The expression is 42x + 36y + 12.
\First find the 42x, 36y and 12.
\Factor the each monomial and Circle the common prime factors.
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GCF : 2 · 3 or 6.
\Write each term as the product of the GCF and its remaining factors.Then use the Distributive Property to factor out the GCF.
\42x + 36y + 12 = 6(7 · x) + 6(2 · 3 · y) + 6(2)
\= 6(7x) + 6(6y) + 6(2)
\= 6(7x + 6y + 2).
\The completely factored form of 42x + 36y + 12 is 6(7x + 6y + 2).