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 π = β4, evaluate π(π₯ + 6) + π(π β 6π₯) β π(π β 5π₯).

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### Video Transcript

Given that π is equal to negative four, evaluate π multiplied by π₯ plus six plus π multiplied by π minus six π₯ minus π multiplied by π 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 π by π₯ and π by six. We would repeat this for the other two sets of parentheses. An alternative method would be to notice that π is a common factor of all three terms. We could therefore factor out a π. Inside our square brackets, weβre left with π₯ plus six plus π minus six π₯ minus π minus five π₯. Removing these brackets, we are left with π₯ plus six plus π minus six π₯ minus π plus five π₯.

We need to take care with the last set of parentheses as weβre in effect multiplying by negative one. Negative one multiplied by π is negative π, and negative one multiplied by negative five π₯ is positive five π₯. We notice here that the πβs cancel. Positive π minus π is zero. The π₯β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 π multiplied by six or six π. We are told in the question that π 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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