Question

Factorise the following:

42a²bc⁴ – 56a³b²c³

Answer 1

Given expression: 42a²bc⁴ – 56a³b²c³

Step-wise calculation:

1. Find the highest common factor (HCF) of the numerical coefficients 42 and 56:

• HCF of 42 and 56 is 14.

2. Find the common variables with the lowest powers in both terms:

• For a² and a³, the lower power is a².
• For b and b², the lower power is b.
• For c⁴ and c³, the lower power is c³.

3. Take out the common factor 14a²bc³.

4. Divide each term by 14a²bc³:

• 42a²bc⁴ ÷ 14a²bc³ = 3c
• 56a³b²c³ ÷ 14a²bc³ = 4ab

5. Write the factored form as 14a²bc³(3c – 4ab).