The shortest form of a3-b3-a2-a b-b2 is

It is given, the algebraic fraction to be: (a^3 + b^3)/(a^2 ab+b^2) Here, we can go for the identities as: (a^3 + b^3) = (a + b)(a^2 ab+b^2) ⇒ The term (a^2 ab+ ...

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Standard VIII

Mathematics

Like and Unlike Terms

The shortest ...

Question

The shortest form of $\frac{(a^{3} + b^{3})}{(a^{2} - a b + b^{2})}$ is ___.

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Solution

It is given, the algebraic fraction to be: $\frac{(a^{3} + b^{3})}{(a^{2} - a b + b^{2})}$

Here, we can go for the identities as: $(a^{3} + b^{3}) = (a + b) (a^{2} - a b + b^{2})$

$\Rightarrow$ The term $(a^{2} - a b + b^{2})$ is common for numerator and denominator as well. Hence, we can strike off the common term.

$\Rightarrow$ The lowest form is: a+b

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Similar questions

Expand the following formulas

(a + b)^{2}

(a - b)^{2}

(a^{2} + b^{2})

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

Q. Factorise :

(a^{2} - b^{2}) (a^{2} + a b + b^{2}) - a^{3} + b^{3}

Q. Simplify

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

is equal to

Q. Expand

a^{3} b^{2}, a^{2} b^{3}, b^{2} a^{3}, b^{3} a^{2} .

Are they all same?

The lowest form of the $\frac{a^{2} - b^{2}}{a^{3} - b^{3}}$ is___

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The shortest form of (a3 + b3)(a2−ab+b2) is ___.

It is given, the algebraic fraction to be: (a3 + b3)(a2−ab+b2) Here, we can go for the identities as: (a3 + b3) = (a + b)(a2−ab+b2) ⇒ The term (a2−ab+b2) is common for numerator and denominator as well. Hence, we can strike off the common term. ⇒ The lowest form is: a+b

The shortest form of $\frac{(a^{3} + b^{3})}{(a^{2} - a b + b^{2})}$ is ___.