Math, asked by Anonymous, 1 year ago

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Q___⬇️Prove the Following Equation ⬇️

==>} a³+b³= (a+b) (a²-ab+b²)

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Answers

Answered by Anonymous
10

Step-by-step explanation:

Heya Mate

a³ + b³ = (a + b)(a² – ab + b²)

we know that , (a + b)^3 = a^3+ 3ab(a + b) + b^3

then a^3 + b^3= (a+ b)^3– 3ab(a + b)

= (a + b)[(a + b)^2 – 3ab]

= (a + b)(a^2 + 2ab + b^2 – 3ab)

= (a + b)(a^2 – ab + b^2 )

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Answered by Brâiñlynêha
10

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To prove:-

\sf a{}^{3}+b{}^{3}=(a+b)(a{}^{2}-ab+b{}^{2})

Then :-

\sf (a+b){}^{3}=a{}^{3}+b{}^{3}+3ab(a+b)

\sf (a{}^{3}+b{}^{3})=(a+b){}^{3}-3ab(a+b)

\sf Take\: (a+b)\: common

\sf (a+b)×[(a+b){}^{2}-3ab]

\sf (a+b)(a{}^{2}+2ab+b{}^{2}-3ab)

\sf (a+b)(a{}^{2}-ab+b{}^{2})

\sf (a{}^{3}+b{}^{3})=(a+b)(a{}^{2}-ab+b{}^{2})

Hence proved!

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