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Chapter 8: Problem 141

Subtract \(3 x^{4} y^{3}+5 x^{2} y-4 x y+5 x-3\) from the polynomial \(5 x^{4} y^{3}-3 x^{2} y+7\)

Short Answer

Expert verified
\(2x^4y^3 - 8x^2y - 4xy + 5x + 4\)

Step by step solution

01

Identify like terms

In both polynomials, look for terms with the same variables and exponents. In our case, the like terms between the two polynomials are: - \(x^4y^3\) terms: \(5x^4y^3\) and \(3x^4y^3\) - \(x^2y\) terms: \(-3x^2y\) and \(5x^2y\) There are some other terms that appear only in the second polynomial: - \(-4xy\) - \(5x\) - \(-3\)
02

Subtract like terms

Subtract the corresponding coefficients of the like terms: - For \(x^4y^3\) terms: \(5 - 3 = 2\) - For \(x^2y\) terms: \(-3 - 5 = -8\)
03

Write down the result

Now, write the resulting polynomial by combining the results of subtracting like terms and the terms that appeared only in the second polynomial: Result: \(2x^4y^3 - 8x^2y - 4xy + 5x - 3 + 7\)
04

Simplify the expression

Combine the constant terms: \(-3 + 7 = 4\) Final result: \(2x^4y^3 - 8x^2y - 4xy + 5x + 4\)

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