Question

Factorise the expression
15 a³b + 35ab³.

Answer 1

The expression 15 a³b + 35ab³ is factorised by finding the GCD of the coefficients and the HCF of the variables, resulting in the factored form 5ab(3a² + 7b²).

Step-by-step explanation:

To factorise the expression 15 a³b + 35ab³, we first look for the greatest common divisor (GCD) of the coefficients and the highest common factor (HCF) of the variables in both terms.

The coefficients 15 and 35 share a GCD of 5. Looking at the variables, we see that both terms include an a and a b. The lowest power of a is 1 and the lowest power of b is also 1, so we can factor out ab from both terms.

Dividing each term by 5ab gives us:

• 15 a³b / 5ab = 3a²
• 35ab³ / 5ab = 7b²

Thus, the factored form of the expression is 5ab(3a² + 7b²).