Question

factorise the following r⁴+27p³r​

Answer 1

Factoring: r³ + 27p³r

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${\tt{\red{\underline{\underline{\huge{Answer:}}}}}}$

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Theory :

• A sum of two perfect cubes, a3 + b3 can be factored into :

$\sf\green{ (a+b) • (a2-ab+b2)}$

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Proof :

(a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

$\sf\color{blue}{→a3+b3}$

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Check :

• 27 is the cube of 3

Check :

• r3 is the cube of r1

Check :

• p3 is the cube of p1

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Factorization is :

$\mathrm{\boxed{\boxed{\pink{→ (r + 3p) • (r2 - 3rp + 9p2) ✔}}}}$

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${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$