Question

factorise 64a³ - 27b³ - 144a²b + 108ab²​

Answer 1

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›»› The expression = (4a - 3b)³

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• 64a³ - 27b³ - 144a²b + 108ab²

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• Factorize the expression.

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Let's start solving the factorization and understand the steps to get our final result.

⇛ 64a³ - 27b³ - 144a²b + 108ab²

Short the polynomial expression in descending order,

⇛ 64³ - 144a²b + 108ab² - 27b³

Do factorization,

⇛ (4a - 3b)³

Hence Solved !

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✒ Factozisation :

Factorizing is to make a single term: try to write everything as products (multiplication), for example:

→ 6x² - 9x + 10 = (2x - 5) (3x - 2)

Step ① :

Find a common factor

Example:

→ 4xy + x⁴ + x = x(4x + x³ + 1)

Step ② :

Count the number of terms

(terms are separated by + or −)

If none of these methods work, re-arrange the terms, or remove brackets and start again.

Answer 2

Answer:

(4a-3b)^3

Step-by-step explanation:

(a-b)^3 = a^3-b^3-3a^2b+3ab^2

=> (4a)^3-(3b)^3-3*(4a)^2*3b+3*4a*(3b)^2

=> (4a-3b)^3 is the answer.