Question

The sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab 2. if one addend is –5a2b2 12a2b – 5, what is the other addend? 15a2b2 – 20a2b 6ab2 – 4ab 7 5a2b2 – 20a2b2 7 5a2b2 4a2b2 6ab – 4ab – 3 –15a2b2 20a2b2 – 6ab 4ab – 7

Answer 1

The other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab  is 15a²b²- 20a²b + 6ab² - 4ab + 7.

What is polynomial?

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The sum of two polynomials is,

$10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2$

The one polynomial addend is,

$-5a^2b^2 +12a^2b - 5$

Let suppose the other polynomial addend is f(a,b). Thus,

$(-5a^2b^2 +12a^2b - 5)+f(a,b)=(10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2)$

Isolate the second polynomial as,

$f(a,b)=(10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2)-(-5a^2b^2 +12a^2b - 5)\\f(a,b)=10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2+5a^2b^2 -12a^2b + 5$

Arrange the like terms as,

$f(a,b)=10a^2b^2+5a^2b^2 - 8a^2b -12a^2b+ 6ab^2 - 4ab + 2+5\\f(a,b)=15a^2b^2- 20a^2b + 6ab^2 - 4ab + 7$

Hence, the other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab  is 15a²b²- 20a²b + 6ab² - 4ab + 7.

Learn more about polynomial here;

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