Question Video: Factorizing a Linear Algebraic Expression by Taking Out the GCF | Nagwa Question Video: Factorizing a Linear Algebraic Expression by Taking Out the GCF | Nagwa

Question Video: Factorizing a Linear Algebraic Expression by Taking Out the GCF Mathematics • First Year of Preparatory School

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Factor the expression 4𝑏𝑐 + 2𝑏𝑑 completely.

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Video Transcript

Factor the expression four 𝑏𝑐 plus two 𝑏𝑑 completely.

In this question, we are given an algebraic expression that we are asked to factor completely. This means that we need to find every nontrivial common factor among the terms so that we cannot factor any further.

To do this, let’s check for common factors among the coefficients and variables separately. We can start by checking for the greatest common divisor of the coefficients. We can note that the greatest common divisor of four and two is two. So we can take out a common factor of two out of the expression.

We can also check for common factors among the variables. We note that the first term only has factors of 𝑏 and 𝑐. So we check the second term for these factors. We see that the second term has a factor of 𝑏 but not 𝑐. So we can take out a factor of 𝑏 from the expression. We call two 𝑏 the greatest common factor of the terms, since we cannot take out any more factors from the terms. We can then take this factor out to obtain two 𝑏 times two 𝑐 plus 𝑑.

We can then check that we cannot factor the expression any further to confirm that the expression is fully factored. Hence, our answer is two 𝑏 multiplied by two 𝑐 plus 𝑑.

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