Question

The difference of two numbers is -15a${}^3$+8a${}^2$-5a+3. If the larger one is 20a${}^3$+10a${}^2$+6a-6, find the smaller number.

• A. 20a³+2a²+3a-9
• B. 35a³+2a²+11a+9
• C. 35a³-2a²-11a+9
• D. 35a³+2a²+11a-9

Answer 1

The correct option is D

35a³+2a²+11a-9

The smaller number is obtained by subtracting the difference from the larger number.

20a${}^3$+10a${}^2$+6a-6-(-15a${}^3$+8a${}^2$-5a+3)

= 20a${}^3$+10a${}^2$+6a-6+15a${}^3$-8a${}^2$+5a-3

= 20a${}^3$+15a${}^3$+10a${}^2$-8a${}^2$+6a+5a-6-3

= 35a${}^3$+2a${}^2$+11a-9