Question Video: Evaluating Algebraic Expressions Involving Factorization by Taking Out the Highest Common Factor

If 5π β 3π = β3 and 2π + 3π = β4, what is the value of 12π + 6π β 10π + 8π?

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Video Transcript

If five π minus three π is equal to negative three and two π plus three π is equal to negative four, what is the value of 12π plus six π minus 10π plus eight π?

The sum of the four terms 12π, six π, negative 10π, and eight π can be written in any order. This means that 12π plus six π minus 10π plus eight π is equal to negative 10π plus six π plus eight π plus 12π.

Letβs begin by considering one of the equations in the question, five π minus three π is equal to negative three. We can multiply both sides of this equation by negative two. This gives us negative 10π plus six π is equal to six. We recall that when multiplying two negative terms, we get a positive answer. The left-hand side here corresponds to the first two terms of our new expression. Negative 10π plus six π is equal to six.

Letβs now consider the second equation we are given, two π plus three π is equal to negative four. We can multiply both sides of this equation by four. On the left-hand side, we have eight π plus 12π. On the right-hand side, we have negative 16. This means that we can replace eight π plus 12π in our expression with negative 16. Adding negative 16 to six is the same as subtracting 16 from six. This is equal to negative 10.

If five π minus three π is equal to negative three and two π plus three π is negative four, then 12π plus six π minus 10π plus eight π is equal to negative 10.