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Big Ideas Math Algebra 1 A Bridge to Success
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Big Ideas Math Algebra 1 A Bridge to Success View details
1. Adding and Subtracting Polynomials
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Exercise 3 Page 357

Consider a particular example and simplify it by using the properties you already know, like the Commutative Property of Addition and the Distributive Property. What can you conclude?

See solution.

Practice makes perfect
Let's consider an example. Imagine that we need to add the polynomials 3x^2+7 and 4x^2-5. (3x^2+7) + (4x^2-5) = 3x^2+7 + 4x^2-5 By using the Commutative Property of Addition we can rearrange the resulting polynomial to have like terms together. Recall that like terms are those that contain the same variables raised to the same power, even if their coefficients do not match.

(3x^2+7) + (4x^2-5) &= 3x^2+7 + 4x^2-5 (3x^2+7) + (4x^2-5) &= 3x^2+ 4x^2+7-5 Now we can rewrite this expression by using the Distributive Property. Then we can continue to simplify the expression. (3x^2+7) + (4x^2-5) &= 3x^2+ 4x^2+7-5 (3x^2+7) + (4x^2-5) &= x^2(3+4)+7-5 (3x^2+7) + (4x^2-5) &= 7x^2+2 As we can see, this is equivalent to adding or subtracting the coefficients of the like terms directly. We can conclude our results as shown below.

To add or subtract polynomials we just need to add or subtract the corresponding like terms.

Subchapter links expand_more
arrow_right Communicate Your Answer p.357
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arrow_right Monitoring Progress p.358-361
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arrow_right Exercises p.362-364
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