Question

2. In the product of (4a3 + 5a2 – 11a) and (-15 + 3a – 7a2), the co-efficient of a4 is …………………… .

Answer 1

The only pairs that will give you some multiple of $a^4$ are:

$4a^3\cdot (3a),\quad 5a^2\cdot(-7a^2)$

their values are respectively

$12a^4,\quad -35a^4$

and their sum is $-23a^4$

Answer 2

Answer:

- 23

Step-by-step explanation:

We could do this the long way and expand the whole product or note that the $a^{4}$ terms arise from the product of the a³ and a terms and the product of the a² and a² terms, that is

4a³ × 3a = 12$a^{4}$

+ 5a² × - 7a² = - 35$a^{4}$

Summing gives

12$a^{4}$ - 35$a^{4}$ = - 23$a^{4}$

with coefficient - 23