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 + 75a2b2 – 20a2b2 + 7 5a2b2 + 4a2b2 + 6ab – 4ab – 3–15a2b2 + 20a2b2 – 6ab + 4ab – 7

Answer:[tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]Step-by-step explanation:The sum of two polynomials is[tex]10a^2b^2-8a^2b+6ab^2-4ab+2[/tex]First addend is[tex]-5a^2b^2+12a^2b-5[/tex]Second addend x.Hence,[tex]x+(-5a^2b^2+12a^2b-5)=10a^2b^2-8a^2b+6ab^2-4ab+2\\ \\x=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)=\\ \\=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5=\\ \\=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)=\\ \\=15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]