8x3 + 27y3 - 216z3 + 108xyz

8x³ + 27y³ - 216z³ + 108xyz

= (2x)³ + (3y )³ + (-6z )³ - 3(2x)(3y )(-6z )

= (2x + 3y + (-6z ))((2x)² + (3y )² + (-6z )² - 2x × 3y - 3y (-6z ) - (-6z )2x)

= (2x + 3y - 6z )(4x² + 9 y² + 36z² - 6xy +18 yz +12zx)

∴ 8x³ + 27 y³ - 216z³ +108xyz = (2x + 3y - 6z )(4x² + 9 y² + 36z² - 6xy +18 yz +12zx)

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अध्याय 5: Factorisation of Algebraic Expressions - Exercise 5.4 [पृष्ठ २३]

अध्याय 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 5 | पृष्ठ २३

Factorize the following expressions:

10x⁴y – 10xy⁴

Factorize 125x³ - 27 y³ - 225x² y +135xy²

Factorize 8a³+ 27b³ + 36a²b + 54ab²

125 + 8x³ - 27 y³ + 90xy

If 3x + 5y = 11 and xy = 2, find the value of 9x²+ 25y²

If a² + b² + c² = 250 and ab + bc + ca = 3, find a + b + c.

If (x + y)³ − (x − y)³ − 6y(x² − y²) = ky², then k =

Write the number of the term of the following polynomial.

5x² + 3 x ax

The total number of planets of Sun can be denoted by the variable n.

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