Question

Factorize: x^3+125y^3​

Answer 1

AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• X³+125y³

${\sf{\green{\underline{\large{To\:find}}}}}$

• Factorize the given term

${\sf{\pink{\underline{\Large{Explanation}}}}}$

we know that

a³+b³ = (a+b) (a²+b²-ab)

Now breaking the given term

(X)³+(5y)³

=>(X)³+(5y)³= (x+5y) (x²+25y²-5xy)

Hence the factorisation of (X)³+(5y)³ is (x+5y) (x²+25y²-5xy)

Additional Information

• a²-b²=(a+b)(a-b)
• a³-b³ =(a-b) (a²+b²+ab)

Answer 2

$\underline{\boxed{ \underline{ \large{ \text{Question}}}}}$

Factorize: x³ + 125y³

$\underline{\boxed{ \underline{\large{ \text{Answer}}}}}$

125y³ can be written as (5y)³

We know that,

$\underline {\boxed{ \textsf{{a}}^{3} + \textsf{{b}}^{3} = \textsf{(a + b)} \textsf{( {a}}^{2} - \textsf{ ab} + \textsf{{b}}^{2} \textsf) }}$

Here,

a = x

b = 5y

So,

$\small {x}^{3} + 125y {}^{3} = (x + 5y)( {x}^{2} - x \times 5y + {(5y)}^{2} ) \\ \\ \implies \boxed{\green{ (x + 5y)( {x}^{2} - 5xy + 25 {y}^{2} )}}$

Hence, the required factorisation is

(x+5y)(x²+25y²-5xy)

_________________

• Related formula:

a³- b³=(a -b)(a² +ab +b²)