Question

Factorisation.

1-) ab + 5a - b - 5
2-) m^2n^2 + m^2 + n^2 + 1
3-) 3xy^2 - 6y^2 + 4x - 8
4-) 6y^3 - 24y^2 + 2y- 8
5-) a^2c + c + a + a^3 - 2 a^2b -2b​

Answer 1

Answer:

. 2x2 and 12x2

Solution:

We know that the numerical coefficients of given numerical are 2 and 12

The greatest common factor of 2 and 12 is 2

The common literals appearing in given monomial is x

The smallest power of x in two monomials is 2

The monomial of common literals with smallest power is x2

∴ The greatest common factor = 2x2

2. 6x3y and 18x2y3

Solution:

We know that the numerical coefficients of given numerical are 6 and18

The greatest common factor of 6 and 18 is 6

Common literals appearing in given numerical are x and y

Smallest power of x in three monomial is 2

Smallest power of y in three monomial is 1

Monomial of common literals with smallest power is x2y

∴ The greatest common factor = 6x2y

3. 7x, 21x2 and 14xy2

Solution:

We know that the numerical coefficients of given numerical are 7, 21 and 14

Greatest common factor of 7, 21 and 14 is 7

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 1

Smallest power of y in three monomials is 0

Monomials of common literals with smallest power is x

∴ The greatest common factor = 7x

4. 42x2yz and 63x3y2z3

Solution:

We know that the numerical coefficients of given numerical are 42 and 63.

Greatest common factor of 42, 63 is 21.

Common literals appearing in given numerical are x, y and z

Smallest power of x in two monomials is 2

Smallest power of y in two monomials is 1

Smallest power of z in two monomials is 1

Monomials of common literals with smallest power is x2yz

∴ The greatest common factor = 21x2yz

5. 12ax2, 6a2x3 and 2a3x5

Solution:

We know that the numerical coefficients of given numerical are 12, 6 and 2

Greatest common factor of 12, 6 and 2 is 2.

Common literals appearing in given numerical are a and x

Smallest power of x in three monomials is 2

Smallest power of a in three monomials is 1

Monomials of common literals with smallest power is ax2

∴ The greatest common factor = 2ax2