Factorisation Test - 9

The given expressions can be factorized as:

9l²mn = 1 × 3 × 3 × l × l × m × n

− 6lm²n = − 1 × 2 × 3 × l × m × m × n

12lmn² = 1 × 2 × 2 × 3× l × m × n × n

Thus, 3l²m is not a common factor of the given expressions.

The correct answer is A.

24l²n² − 40l³n

= 8l²n × 3n − 8l²n × 5l

= 8l²n (3n − 5l)

Thus, the given expression can be factorized as 8l²n (3n − 5l).

The correct answer is C.

6a³ + 8a² + 3ab + 4b

= 2a²(3a + 4) + b(3a + 4)

= (3a + 4) (2a²+ b)

Thus, the given expression can be factorized as (3a + 4) (2a²+ b).

Hence, the correct answer is option D.

The given expression is (y² − 21y − 72).

It can be seen that −72 = −24 × 3 and −21 = (−24 +3)

∴ y² − 21y − 72 = y² + {(− 24) + 3} y + (− 24) × 3

This is of the form x² + (a + b) x + ab, where x = y, a = −24, and b = 3.

We know that,

x² + (a + b) x + ab = (x + a) (x + b)

∴ y² + {(− 24) + 3} y + (− 24) × 3 = (y − 24) (y + 3)

Thus, the factorized form of the expression (y² − 21y − 72) is (y − 24) (y + 3).

The correct answer is A.

(2x − y) ⁴ − y⁴

= {(2x − y) ²}² − (y²)²

= [(2x − y) ² + y²] [(2x − y) ² − y²] [a² − b² = (a + b) (a − b)]

= [4x² + y² − 4xy + y²] [(2x − y) + y] [(2x − y) − y]

= (4x² + 2y² − 4xy) (2x) (2x − 2y)

= 2 (2x² + y² − 2xy) × 2x × 2(x − y)

= 8x(x − y) (2x² + y² − 2xy)

The correct answer is D.

16y² − x² − 24y + 9

= (16y² − 24y + 9) − x²

= [(4y) ² − 2 × 4y × 3 + 3²] − x²

= (4y − 3)² − x² [a²− 2ab + b² = (a − b) ²]

= [(4y − 3) − x] [(4y − 3) + x]

= (4y − 3 − x) (4y − 3 + x) [a² − b² = (a + b) (a − b)]

The correct answer is A.

We can write the given expression as:

872² + 28² + 2 × 872 × 28

This expression is of the form a² + b² + 2ab, where a = 872 and b = 28.

We know that,

(a + b) ² = a² + b² + 2ab

∴ 872² + 28² + 48832 = (872 + 28)²

= (872 + 28) (872 + 28)

The correct answer is B.

192x² − 75x⁴

= 3x² (64 − 25x²)

= 3x² [8² − (5x) ²]

= 3x² (8 + 5x) (8 − 5x) [a² − b² = (a + b) (a − b)]

The correct answer is A.

e² + 4f ² + 4ef − 16

= [e² + 4ef + 4f ²] − 16

= [e² + 2 × e × (2f) + (2f) ²] − 16

= (e +2f) ² − 4² [a² + 2ab + b² = (a + b)²]

= (e + 2f − 4) (e + 2f + 4) [a² − b² = (a − b) (a + b)]

The correct answer is B.

7x³y + 14xy² − 28xy

= 7xy × x² + 7xy × 2y − 7xy × 4

= 7xy (x² + 2y − 4)

Thus, the given expression can be factorized as 7xy (x² + 2y − 4).

The correct answer is A.

The given expression (2a³ + 6a² − ab + 2a − 3b + 6) can be rearranged as:

2a³ + 6a² − ab − 3b + 2a + 6

= 2a² (a + 3) − b (a + 3) + 2 (a + 3)

= (a + 3) (2a² − b + 2)

The correct answer is A.