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Mathematics

Divide:

4a2 + 12ab + 9b2 - 25c2 by 2a + 3b + 5c

Algebraic Expressions

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Answer

Dividing 4a2 + 12ab + 9b2 - 25c2 by 2a + 3b + 5c

2a+3b+5c)2a+3b−5c2a+3b+5c)4a2+12ab+9b2−25c2‾2a+3b+5c−4a2+−6ab+9b2−25c2+−10ac‾2a+3b+5c2x3+6ab−10ac+9b2−25c22a+3b+5c2x+−6ab−10ac+−9b2−25c2+−15bc‾2a+3b+5c2x3++5x2+−10ac−25c2−15bc2a+3b+5c2x3++5x2+−+10ac−+25c2−+15bc‾2a+3b+5c2x3++5x2+−23x×\begin{array}{l} \phantom{2a + 3b + 5c)}{2a + 3b - 5c} \ 2a + 3b + 5c\overline{\smash{\big)}4a^2 + 12ab + 9b^2 - 25c^2} \ \phantom{2a + 3b + 5c}\underline{\underset{-}{}4a^2 \underset{-}{+}6ab \phantom{+ 9b^2 - 25c^2} \underset{-}{+}10ac} \ \phantom{{2a + 3b + 5c}2x^3+}6ab - 10ac + 9b^2 - 25c^2 \ \phantom{{2a + 3b + 5c}2x+}\underline{\underset{-}{}6ab \phantom{- 10ac} \underset{-}{+} 9b^2 \phantom{- 25c^2} \underset{-}{+} 15bc} \ \phantom{{2a + 3b + 5c}{2x^3+}{+5x^2+}}-10ac - 25c^2 -15bc \ \phantom{{2a + 3b + 5c}{2x^3+}{+5x^2+\enspace}}\underline{\underset{+}{-}10ac \underset{+}{-} 25c^2 \underset{+}{-} 15bc} \ \phantom{{2a + 3b + 5c}{2x^3+}{+5x^2+\qquad}{-23x}}\times \end{array}

Hence, (4a2 + 12ab + 9b2 - 25c2) ÷ (2a + 3b + 5c) = 2a + 3b - 5c

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