Question

factorise
$\frac{ {x}^{3} }{64} + \frac{ {z}^{3} }{27} + \frac{xz}{4} ( \frac{x}{4} + \frac{z}{3} )$
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Answer 1

Qᴜᴇsᴛɪᴏɴ :-

• Factorise :- (x³/64) + (z³/27) + (xz/4)[(x/4) + (z/3)]

Sᴏʟᴜᴛɪᴏɴ :-

→ (x³/64) + (z³/27) + (xz/4)[(x/4) + (z/3)]

→ (x/4)³ + (z/3)³ + (x/4) * z * [(x/4) + (z/3)]

Multiply & Divide by 3

→ (x/4)³ + (z/3)³ + 3 * (x/4) * (z/3) * [(x/4) + (z/3)]

Comparing it with , a³ + b³ + 3 * a * b [ a + b ] = (a + b)³

→ a = (x/4)

→ b = (z/3)

So,

→ [(x/4) + (z/3)]³

→ [(x/4) + (z/3)] * [(x/4) + (z/3)] * [(x/4) + (z/3)] (Ans.)

Answer 2

SOLUTION:-

→ x³/64 + z³/27 + xz/4 (x/4 + z/3)

→ (x/4)³ + (z/3)³ + (x/4) × z × [(x/4) + (z/3)]

Multiplying and dividing with 3

→ (x/4)³ + (z/3)³ + 3 × (x/4) × (z/3) × [(x/4) + (z/3)]

It is in the form of (a + b)³ = a³ + b³ + 3ab(a + b)

Then,

→ [(x/4) + (z/3)]³

Using

♦ (a + b)³ = (a + b)(a + b)(a + b)

→ [(x/4) + (z/3)] × [(x/4) + (z/3)] × [(x/4) + (z/3)]

Hence , factorised