Question

simplify the following :(a-2b+5c)(a-b)-(a-b-c)(2a+3c)+(6a+b)(2c-3a-5b)​

Answer 1

The given expression is:

(a - 2b + 5c)(a - b) - (a - b - c)(2a + 3c) + (6a + b)(2c - 3a - 5b)​

We have to simplify the given expression.

Solution:

∴ (a - 2b + 5c)(a - b) - (a - b - c)(2a + 3c) + (6a + b)(2c - 3a - 5b)​

= {a(a - b) - 2b(a - b) + 5c(a - b)} - {a(2a + 3c) - b(2a + 3c) - c(2a + 3c)} + {6a(2c - 3a - 5b)​ + b(2c - 3a - 5b)​}

= {$a^{2}$ - ab - 2ab + 2$b^{2}$ + 5ac - 5bc} - {2$a^{2}$ + 3ac - 2ab - 3bc - 2ac - 3$c^{2}$} +

{12ac - 18$a^{2}$ - 30ab + 2bc - 3ab - 5$b^{2}$}

= $a^{2}$ - ab - 2ab + 2$b^{2}$ + 5ac - 5bc - 2$a^{2}$ - 3ac + 2ab + 3bc + 2ac + 3$c^{2}$ +

12ac - 18$a^{2}$ - 30ab + 2bc - 3ab - 5$b^{2}$

= - 19$a^{2}$ - 3$b^{2}$ + 3$c^{2}$ - 34ab + 0(bc) + 16ac

= - 19$a^{2}$ - 3$b^{2}$ + 3$c^{2}$ - 34ab + 16ac

∴ (a - 2b + 5c)(a - b) - (a - b - c)(2a + 3c) + (6a + b)(2c - 3a - 5b)​ =  - 19$a^{2}$ - 3$b^{2}$ + 3$c^{2}$ - 34ab + 16ac

Thus, the simplification of (a - 2b + 5c)(a - b) - (a - b - c)(2a + 3c) + (6a + b)(2c - 3a - 5b)​ is "- 19$a^{2}$ - 3$b^{2}$ + 3$c^{2}$ - 34ab + 16ac".

Answer 2

Answer:

Given:

(a-2b+5c)(a-b)-(a-b-c)(2a+3c)+(6a+b)(2c-3a-5b)

Step-by-step explaination:

(a-2b+5c)(a-b)-(a-b-c)(2a+3c)+(6a+b)(2c-3a-5b)

=[$a^{2}$-2ab+5ac-ab+2$b^{2}$-5bc]-[2$a^{2}$+3ac-2ab-3bc-2ac-3$c^{2}$]+[12ac-18$a^{2}$-30ab+2bc-3ab-5$b^{2}$]

=$a^{2}$-2$a^{2}$-18$a^{2}$+2$b^{2}$-5$b^{2}$-3$c^{2}$-2ab-ab-2ab-30ab-3ab+5ac+12ac+3ac-2ac-5bc-3bc+2bc

=$a^{2}$(1-12-18)+$b^{2}$(2-5)+$c^{2}$(-3)+ab(-2-1-2-30-3)+ac(5+12+3-2)+bc(-5-3+2)

= -29$a^{2}$-3$b^{2}$-3$c^{2}$-38ab+18ac-6bc