Video: Factoring by Taking Out Common Factors

Factor the expression 4𝑏𝑐 + 2𝑏𝑑 completely.

01:25

Video Transcript

Factor the expression four 𝑏𝑐 plus two 𝑏𝑑 completely.

In order to factor or factorise an expression, we need to find the highest common factor of the two terms. The highest common factor of four and two is two. Therefore, we need to take two out of the parenthesis. 𝑏 is also common to the two terms four 𝑏𝑐 and two 𝑏𝑑. Therefore, we need to take 𝑏 out of the parenthesis.

Four 𝑏𝑐 divided by two 𝑏 is equal to two 𝑐. This means that the first term in the parenthesis is two 𝑐. Two 𝑏𝑑 divided by two 𝑏 is equal to 𝑑. Therefore, the second term inside the parenthesis is 𝑑. Four 𝑏𝑐 plus two 𝑏𝑑 factored completely is equal to two 𝑏 multiplied by two 𝑐 plus 𝑑.

We could check this answer by expanding the brackets or parenthesis. Two 𝑏 multiplied by two 𝑐 is equal to four 𝑏𝑐. And two 𝑏 multiplied by 𝑑 is equal to two 𝑏𝑑.

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