Answer:
- 23
Step-by-step explanation:
We could do this the long way and expand the whole product or note that the [tex]a^{4}[/tex] 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[tex]a^{4}[/tex]
+ 5a² × - 7a² = - 35[tex]a^{4}[/tex]
Summing gives
12[tex]a^{4}[/tex] - 35[tex]a^{4}[/tex] = - 23[tex]a^{4}[/tex]
with coefficient - 23
The only pairs that will give you some multiple of [tex]a^4[/tex] are:
[tex]4a^3\cdot (3a),\quad 5a^2\cdot(-7a^2)[/tex]
their values are respectively
[tex]12a^4,\quad -35a^4[/tex]
and their sum is [tex]-23a^4[/tex]
