Question

a3+b3+3ab(a+b)=(a+b)3 how to prove​

Answer 1

Answer:

Proof :-

(a+b)³ = a³+b³ × 3ab(a+b)

subtract 3ab(a+b) both side

☞ a³ + b³ = (a+b)³ - 3ab(a+b)

Take (a+b) as common

☞ a³ + b³ = (a+b)((a+b)² - 3ab)

Expand (a+b)²

☞ a³ + b³ = (a + b)(a² - b² + 2ab - 3ab)

☞ a³ + b³ = (a+b)( a² - ab + 3b²)

Hence Proved

LHS = RHS

Step-by-step explanation:

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Answer 2

Given data: $a^{3} +b^3+3ab(a+b)=(a+b)^3$

To prove: The cubic formula.

Solution:

• According to the cubic formula, We can prove by LHS=RHS.
• Considering the RHS, We have $(a+b)^3$.
• Expanding the cube we get $(a+b)(a+b)(a+b)$.
• $(a+b)^2=a^2+2ab+b^2$ is the cubic formula. Applying the formula in the given equation we have $(a^2+2ab+b^2)(a+b)$.
• Multiplying the values we get $a^3+2a^2b+ab^2+a^2b+b^3+2ab^2$.
• Simplifying the equation $a^3+3a^2b+3ab^2+b^3$.
• Hence the given cubic equation is proved $a^{3} +b^3+3ab(a+b)=(a+b)^3$ (LHS=RHS).