Video Transcript
Given that 𝑏 is equal to negative four, evaluate 𝑏 multiplied by 𝑥 plus six plus 𝑏 multiplied by 𝑐 minus six 𝑥 minus 𝑏 multiplied by 𝑐 minus five 𝑥.
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 𝑥 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 𝑥 plus six plus 𝑐 minus six 𝑥 minus 𝑐 minus five 𝑥. Removing these brackets, we are left with 𝑥 plus six plus 𝑐 minus six 𝑥 minus 𝑐 plus five 𝑥.
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 𝑥 is positive five 𝑥. We notice here that the 𝑐’s cancel. Positive 𝑐 minus 𝑐 is zero. The 𝑥’s also cancel, as 𝑥 minus six 𝑥 is negative five 𝑥, and adding five 𝑥 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.
