Factorise : 1029 - 3x 3

Given, 1029 - 3x 3 = 3(343 - x 3 ) = 3[(7) 3 - (x) 3 ] = 3(7 - x)[(7) 2 + 7x + x 2 ] [∵ a 3 - b 3 = (a - b)(a 2 + ab + b 2 )] = 3(7 - x)(x 2 + 7x + 49). Hence, 1029 - 3x 3 = 3(7 - x)(x 2 + 7x + 49).

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Mathematics

Factorise :
1029 - 3x³

Factorisation

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Answer

Given,

1029 - 3x³

= 3(343 - x³)

= 3[(7)³ - (x)³]

= 3(7 - x)[(7)² + 7x + x²] [∵ a³ - b³ = (a - b)(a² + ab + b²)]

= 3(7 - x)(x² + 7x + 49).

Hence, 1029 - 3x³ = 3(7 - x)(x² + 7x + 49).

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Mathematics

Factorise :
1029 - 3x³

Factorisation

Answer

Related Questions

Factorise :
a²(b + c) - (b + c)³

Factorise :
2x³ + 54y³ - 4x - 12y

Show that :
(i) 13³ - 5³ is divisible by 8.
(ii) 35³ + 27³ is divisible by 62.

Evaluate :
$\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}$

Mathematics

Factorise :1029 - 3x3

Factorisation

Answer

Related Questions

Factorise :a2(b + c) - (b + c)3

Factorise :2x3 + 54y3 - 4x - 12y

Show that :(i) 133 - 53 is divisible by 8.(ii) 353 + 273 is divisible by 62.

Evaluate :5.67×5.67×5.67+4.33×4.33×4.335.67×5.67−5.67×4.33+4.33×4.33\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}5.67×5.67−5.67×4.33+4.33×4.335.67×5.67×5.67+4.33×4.33×4.33​

Factorise :
1029 - 3x³

Factorise :
a²(b + c) - (b + c)³

Factorise :
2x³ + 54y³ - 4x - 12y

Show that :
(i) 13³ - 5³ is divisible by 8.
(ii) 35³ + 27³ is divisible by 62.

Evaluate :
$\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}$