Question

1.) (с+2)(с-3)-(с+3) 2.) (4x-3)^2-6x(4-x) 3.) (a-x)^2+(a+x)^2 4.) 2(x+6)^2-(20x+70)

Answer 1

(с+2)(с-3) -(с+3) = с² - 3с + 2с  - 6  -с - 3 = 
=с²   + ( - 3с -с  + 2с)  - (6+3) = 
= с²  - 2с  - 9

(4х  - 3)²  - 6х(4-х) = (4х)² - 2*4х*3 + 3²  - 24х  + 6х² =
= 16х²  - 24х  + 9   - 24х  + 6х²  = 
= (16х²  + 6х²)  - (24х + 24х)   +  9 =
= 22х² - 48х  + 9

(а-х)² + (а+х)²  = а² - 2ах +х² + а² +2ах + х² = 
= (а²+а²)  + (2ах - 2ах)  + (х² + х²) = 
= 2а² + 2х²

2(х+6)² - (20х + 70) = 2(х² + 2*х*6 + 6²)  - 20х  - 70 =
= 2х² + 24х  + 36  - 20х  - 70  =
= 2х²  + (24х - 20х)  - (70 - 36) =
= 2х²  + 4х   -  34

Answer 2

Let's solve each of the expressions step by step:

1. (c+2)(c-3)-(c+3) Expanding the expression: = c^2 - 3c + 2c - 6 - c - 3 Combining like terms: = c^2 - 2c - 9

2. (4x-3)^2 - 6x(4-x) Expanding the expression: = (16x^2 - 24x + 9) - (24x^2 - 6x^2) = 16x^2 - 24x + 9 - 24x^2 + 6x^2 Combining like terms: = -2x^2 - 24x + 9

3. (a-x)^2 + (a+x)^2 Expanding the expression: = (a^2 - 2ax + x^2) + (a^2 + 2ax + x^2) = a^2 - 2ax + x^2 + a^2 + 2ax + x^2 Combining like terms: = 2a^2 + 2x^2

4. 2(x+6)^2 - (20x+70) Expanding the expression: = 2(x^2 + 12x + 36) - 20x - 70 = 2x^2 + 24x + 72 - 20x - 70 Combining like terms: = 2x^2 + 4x + 2

So the simplified forms of the expressions are:

1. c^2 - 2c - 9
2. -2x^2 - 24x + 9
3. 2a^2 + 2x^2
4. 2x^2 + 4x + 2