Multiply and verify the result for a=-2,b=-1 a. (a²b-5a)(3a+4a²-7ab+1) b. (2ab+4a-a³)(a²+3ab-5)

Asked by deepsikhab71.8cpsb | 23rd Jul, 2021, 01:39: PM

Expert Answer:

Given: a = -2, b = -1
a. (a²b-5a)(3a+4a²-7ab+1)
open parentheses straight a squared straight b minus 5 straight a close parentheses open parentheses 3 straight a plus 4 straight a squared minus 7 ab plus 1 close parentheses
equals 3 straight a cubed straight b minus 15 straight a squared plus 4 straight a to the power of 4 straight b minus 20 straight a cubed minus 7 straight a cubed straight b squared plus 35 straight a squared straight b plus straight a squared straight b minus 5 straight a
equals 3 straight a cubed straight b minus 15 straight a squared plus 4 straight a to the power of 4 straight b minus 20 straight a cubed minus 7 straight a cubed straight b squared plus 36 straight a squared straight b minus 5 straight a

Now comma space straight a squared straight b minus 5 straight a space equals space open parentheses negative 2 close parentheses squared open parentheses negative 1 close parentheses minus 5 open parentheses negative 2 close parentheses equals negative 4 plus 10 equals 6
3 straight a plus 4 straight a squared minus 7 ab plus 1 equals 3 open parentheses negative 2 close parentheses plus 4 open parentheses negative 2 close parentheses squared minus 7 open parentheses negative 2 close parentheses open parentheses negative 1 close parentheses plus 1 equals negative 6 plus 16 minus 14 plus 1 equals negative 3
Therefore comma space open parentheses straight a squared straight b minus 5 straight a close parentheses open parentheses 3 straight a plus 4 straight a squared minus 7 ab plus 1 close parentheses equals open parentheses 6 close parentheses open parentheses negative 3 close parentheses equals negative 18
3 straight a cubed straight b minus 15 straight a squared plus 4 straight a to the power of 4 straight b minus 20 straight a cubed minus 7 straight a cubed straight b squared plus 36 straight a squared straight b minus 5 straight a
equals 3 open parentheses negative 2 close parentheses cubed open parentheses negative 1 close parentheses minus 15 open parentheses negative 2 close parentheses squared plus 4 open parentheses negative 2 close parentheses to the power of 4 open parentheses negative 1 close parentheses minus 20 open parentheses negative 2 close parentheses cubed minus 7 open parentheses negative 2 close parentheses cubed open parentheses negative 1 close parentheses squared plus 36 open parentheses negative 2 close parentheses squared open parentheses negative 1 close parentheses minus 5 open parentheses negative 2 close parentheses
equals 24 minus 60 minus 64 plus 160 plus 56 minus 144 plus 10
equals 250 minus 268
equals negative 18
Hence comma space verified
 
b. (2ab+4a-a³)(a²+3ab-5)
open parentheses 2 ab plus 4 straight a minus straight a cubed close parentheses open parentheses straight a squared plus 3 ab minus 5 close parentheses
equals 2 straight a cubed straight b plus 4 straight a cubed minus straight a to the power of 5 plus 6 straight a squared straight b squared plus 12 straight a squared straight b minus 3 straight a to the power of 4 straight b minus 10 ab minus 20 straight a plus 5 straight a cubed
equals 2 straight a cubed straight b plus 9 straight a cubed minus straight a to the power of 5 plus 6 straight a squared straight b squared plus 12 straight a squared straight b minus 3 straight a to the power of 4 straight b minus 10 ab minus 20 straight a

Now comma space for space straight a space equals space minus 2 space and space straight b space equals space minus 1
2 ab plus 4 straight a minus straight a cubed equals 2 open parentheses negative 2 close parentheses open parentheses negative 1 close parentheses plus 4 open parentheses negative 2 close parentheses minus open parentheses negative 2 close parentheses cubed equals 4 minus 8 plus 8 equals 4
straight a squared plus 3 ab minus 5 equals open parentheses negative 2 close parentheses squared plus 3 open parentheses negative 2 close parentheses open parentheses negative 1 close parentheses minus 5 equals 4 plus 6 minus 5 equals 5
Therefore comma space open parentheses 2 ab plus 4 straight a minus straight a cubed close parentheses open parentheses straight a squared plus 3 ab minus 5 close parentheses equals 4 cross times 5 equals 20

And comma
2 straight a cubed straight b plus 9 straight a cubed minus straight a to the power of 5 plus 6 straight a squared straight b squared plus 12 straight a squared straight b minus 3 straight a to the power of 4 straight b minus 10 ab minus 20 straight a
equals 2 open parentheses negative 2 close parentheses cubed open parentheses negative 1 close parentheses plus 9 open parentheses negative 2 close parentheses cubed minus open parentheses negative 2 close parentheses to the power of 5 plus 6 open parentheses negative 2 close parentheses squared open parentheses negative 1 close parentheses squared plus 12 open parentheses negative 2 close parentheses squared open parentheses negative 1 close parentheses minus 3 open parentheses negative 2 close parentheses to the power of 4 open parentheses negative 1 close parentheses minus 10 open parentheses negative 2 close parentheses open parentheses negative 1 close parentheses minus 20 open parentheses negative 2 close parentheses
equals 16 minus 72 plus 32 plus 24 minus 48 plus 48 minus 20 plus 40
equals 20
Hence comma space verified

Answered by Renu Varma | 29th Jul, 2021, 11:44: PM