Factorize 8/27 X^3 + 1 + 4/3 X^2 + 2x

Factorize `8/27 x^3 + 1 + 4/3 x^2 + 2x`

`= (2/3 x)^3 + (1)^3 + 3 xx (2/3 x)^2 xx 1 + 3(1)^2 xx (2/3 x)`

`= (2/3 x + 1)^3 [∵ a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^2]`

`= (2/3 x + 1)(2/3x + 1)(2/3x + 1)`

`∴ 8/27 x^3 + 1 + 4/3 x^2 + 2x = (2/3x + 1)(2/3 x + 1)(2/3x + 1)`

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अध्याय 5: Factorisation of Algebraic Expressions - Exercise 5.3 [पृष्ठ १७]

अध्याय 5 Factorisation of Algebraic Expressions
Exercise 5.3 | Q 3 | पृष्ठ १७

Factorize `x^2 + 6sqrt2x + 10`

Factorize the following expressions:

8a³ - b³ - 4ax + 2bx

(2x - 3y)³ + (4z - 2x)³ + (3y - 4z )³

The factors of x³ − 1 + y³ + 3xy are

Evaluate: (3x - 1)(4x³ - 2x² + 6x - 3)

When y = –1, the value of the expression 2y – 1 is 3

Write the variables, constant and terms of the following expression

18 + x – y

Which of the following is correct?

Match Column I with Column II in the following:

Column I	Column II
1. The difference of 3 and a number squared	(a) 4 – 2x
2. 5 less than twice a number squared	(b) n² – 3
3. Five minus twice the square of a number	(c) 2n² – 5
4. Four minus a number multiplied by 2	(d) 5 – 2n²
5. Seven times the sum of a number and 1	(e) 3 – n²
6. A number squared plus 6	(f) 2(n + 6)
7. 2 times the sum of a number and 6	(g) 7(n + 1)
8. Three less than the square of a number	(h) n² + 6

In the term 10xyz, what is the numerical coefficient?