Question Video: Evaluating Algebraic Expressions by Factoring out the Highest Common Factor | Nagwa Question Video: Evaluating Algebraic Expressions by Factoring out the Highest Common Factor | Nagwa

Question Video: Evaluating Algebraic Expressions by Factoring out the Highest Common Factor Mathematics

Given that 𝑏 = βˆ’4, evaluate 𝑏(π‘₯ + 6) + 𝑏(𝑐 βˆ’ 6π‘₯) βˆ’ 𝑏(𝑐 βˆ’ 5π‘₯).

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Video Transcript

Given that 𝑏 is equal to negative four, evaluate 𝑏 multiplied by π‘₯ plus six plus 𝑏 multiplied by 𝑐 minus six π‘₯ minus 𝑏 multiplied by 𝑐 minus five π‘₯.

We could begin this question by firstly distributing the parentheses, otherwise known as expanding the brackets. In the first set of parentheses, we would multiply 𝑏 by π‘₯ and 𝑏 by six. We would repeat this for the other two sets of parentheses. An alternative method would be to notice that 𝑏 is a common factor of all three terms. We could therefore factor out a 𝑏. Inside our square brackets, we’re left with π‘₯ plus six plus 𝑐 minus six π‘₯ minus 𝑐 minus five π‘₯. Removing these brackets, we are left with π‘₯ plus six plus 𝑐 minus six π‘₯ minus 𝑐 plus five π‘₯.

We need to take care with the last set of parentheses as we’re in effect multiplying by negative one. Negative one multiplied by 𝑐 is negative 𝑐, and negative one multiplied by negative five π‘₯ is positive five π‘₯. We notice here that the 𝑐’s cancel. Positive 𝑐 minus 𝑐 is zero. The π‘₯’s also cancel, as π‘₯ minus six π‘₯ is negative five π‘₯, and adding five π‘₯ to this gives us zero. We are therefore left with 𝑏 multiplied by six or six 𝑏. We are told in the question that 𝑏 is equal to negative four, so we need to multiply six by negative four. Multiplying a positive by a negative gives a negative. Therefore, our answer is negative 24.

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