Question

a³+b³,a²b-ab²+b³,a⁴+a²b²+b⁴​

Answer 1

$\huge⚘ \bf \ \red{Answer}$

$\Large\underline{\pink{\underline{\frak{\pmb{1) \: \: {a}^{3} + {b}^{3} }}}}}$

a³ + b³ = (a + b)(a² – ab + b²)

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$\Large\underline{\pink{\underline{\frak{\pmb{2) \: \: a²b+a³+b³-ab²}}}}}$

after arranging in this way start factorising

=a²(b+a)-b²(b+a)

we use a subtraction sign before b² with the second value in the bracket to make the values in this bracket similar to the value in first one

we now take the numbers outside the brackets and place them together and also pick a value from the ones in the brackets like this

=(a²-b²) (b+a)

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$\Large\underline{\pink{\underline{\frak{\pmb{3) \: a⁴+a²b²+b⁴}}}}}$

= (a² +b²)² - 2a²b² + a²b²

= (a²+b²)² - a²b²

= (a²+b²)² - (ab)²

now it is in the form of a² - b² =( a+ b)(a-b)

(a²+b²+ab)(a²+b² - ab)

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Answer 2

Answer:

⚘ Answer

\Large\underline{\pink{\underline{\frak{\pmb{1) \: \: {a}^{3} + {b}^{3} }}}}}

1)a

3

+b

3

1)a

3

+b

3

a³ + b³ = (a + b)(a² – ab + b²)

____________________

\Large\underline{\pink{\underline{\frak{\pmb{2) \: \: a²b+a³+b³-ab²}}}}}

2)a²b+a³+b³−ab²

2)a²b+a³+b³−ab²

after arranging in this way start factorising

=a²(b+a)-b²(b+a)

we use a subtraction sign before b² with the second value in the bracket to make the values in this bracket similar to the value in first one

we now take the numbers outside the brackets and place them together and also pick a value from the ones in the brackets like this

=(a²-b²) (b+a)

___________________

\Large\underline{\pink{\underline{\frak{\pmb{3) \: a⁴+a²b²+b⁴}}}}}

3)a⁴+a²b²+b⁴

3)a⁴+a²b²+b⁴

= (a² +b²)² - 2a²b² + a²b²

= (a²+b²)² - a²b²

= (a²+b²)² - (ab)²

now it is in the form of a² - b² =( a+ b)(a-b)

(a²+b²+ab)(a²+b² - ab)