In Exercises 29 –40, add the polynomials. Assume that all variable exponents represent whole numbers. ( 9 x 4 y 2 − 6 x 2 y 2 + 3 x y ) + ( − 18 x 4 y 2 − 5 x 2 y − x y )
In Exercises 29 –40, add the polynomials. Assume that all variable exponents represent whole numbers. ( 9 x 4 y 2 − 6 x 2 y 2 + 3 x y ) + ( − 18 x 4 y 2 − 5 x 2 y − x y )
Solution Summary: The author calculates the sum of the two polynomials by adding the expression and simplifying it.
In Exercises 133–136, factor each polynomial completely. Assume
that any variable exponents represent whole numbers.
133. y + x + x + y
134. 36x2" – y2n
135. x*
3n
12n
136. 4x2" + 20x"y" + 25y2m
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples.
• In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2).
• Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5).
To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that
x + 4 = (x + 2i)(x – 2i).
115. а. х
- 9
116. а. х?
- 100
117. а. х
- 64
b. x + 9
b. + 100
b. x + 64
118. а. х — 25
119. а. х— 3
120. а. х — 11
b. x + 25
b. x + 3
b. x + 11
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