Problem 64
Question
Factor each polynomial using the greatest common binomial factor. $$7 x(x+y)-(x+y)$$
Step-by-Step Solution
Verified Answer
The simplified, factorized form of the polynomial is \((7x-1)(x+y)\).
1Step 1: Identify the common binomial factor
The expression can be rewritten by factoring out the greatest common binomial factor which in this case is \(x+y\). So, the expression becomes \(7x(x+y)-(1)(x+y)\). This makes it easier to identify the binomial common factor.
2Step 2: Redistribute the parentheses
Redistribute the parentheses so that the common binomial factor appears in each term. The expression becomes \(7x*(x+y)-1*(x+y)\). Doing this allows the factorization of the entire polynomial by the common factor.
3Step 3: Factorize and simplify the polynomial
Factor out the common binomial factor to simplify the polynomial. The expression becomes \((7x-1)(x+y)\).
Other exercises in this chapter
Problem 64
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Factor completely. $$36 y^{2}+6 y-12$$
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