Question

Add, $7{{x}^{3}}+2{{x}^{2}}-5x-7\ \And \ -5{{x}^{2}}+{{x}^{3}}+4x-5$.

Answer 1

Hint: To add the given two algebraic expressions, add the coefficients of the same powers of x. Add coefficients of ${{x}^{3}},{{x}^{2}},x$ to get the coefficient of ${{x}^{3}},{{x}^{2}}\ and\ x$ respectively in the sum and add the constant terms together to get the constant term of the sum.

Complete step by step answer:
In the sum there will be terms of ${{x}^{3}},{{x}^{2}},x$ and there will be a constant term, as the two terms have the terms of ${{x}^{3}},{{x}^{2}}\ and\ x$ and also constant terms.
Coefficient of ${{x}^{3}}$ in the sum will be the sum of coefficient of ${{x}^{3}}$ in the given two terms.
Coefficient of ${{x}^{3}}$ in the first expression = 7
Coefficient of ${{x}^{3}}$ in the second expression = 1
So, coefficient of ${{x}^{3}}$ in the sum = 7 + 1 = 8
Similarly,
Coefficient of ${{x}^{2}}$ in the sum will be the sum of coefficient of ${{x}^{2}}$ in the two expressions.
Coefficient of ${{x}^{2}}$ in the first expression = 2
Coefficient of ${{x}^{2}}$ in the second expression = -5
So, the coefficient of ${{x}^{2}}$ in the sum = 2 + (-5) = -3
Similarly,
Coefficient of $x$ in the sum will be the sum of coefficients of $x$ in the two expressions.
Coefficient of $x$ in the first expression = -5
Coefficient of $x$ in the second expression = 4
So, the coefficient of $x$ in the sum = (-5) + (4) = -1
Similarly, the constant term in the sum will be the sum of constants in the two expressions.
Constant term in first expression = -7
Constant term in second expression = -5
So, the constant term in the sum = (-7) +(-5) = -12
Hence, we have found that coefficient of ${{x}^{3}}$ in the sum will be 8, coefficient of ${{x}^{2}}$ in the sum will be -3, coefficient of $x$ in the sum will be -1 and the constant term in the sum will be -12.
Hence, the sum of the two algebraic expressions will be $8{{x}^{3}}-3{{x}^{2}}-x-12$.

Note: Note that we can only add the terms which are having the same powers in $x$. If the terms have different powers in $'x'$, we cannot add them together to make one term but we will simply write the terms together using ‘+’ or ‘ – ‘ sign. As we cannot add $8{{x}^{3}},-3{{x}^{2}},-x\ and-12$ to make one term. So, we will write the sum using these terms with ‘+’ or ‘ – ‘ sign i.e. $8{{x}^{3}}-3{{x}^{2}}-x-12$.