Упр.396 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) 2a^4-ab+2b^2 при a=-1; b=-0,5;
2) x^2+2xy+y^2 при x=1,2; y=-1,2.
Разложить на множители:
1) a^2-b^2+a+b;
2) a^2-b^2-a-b;
3) x-y-x^2+y^2;
4) x^3+x^2-x-1;
5) m^5-m^3+m^2-1;
6) x^4-x^3+x-1.

1. При $$a=-1$$, $$b=-0,5$$:

   $$2a^4-ab+2b^2=2\cdot(-1)^4-(-1)\cdot(-0,5)+2\cdot(-0,5)^2$$

   $$=2\cdot1-0,5+2\cdot0,25=2-0,5+0,5=2.$$

2. При $$x=1,2$$, $$y=-1,2$$:

   $$x^2+2xy+y^2=(1,2)^2+2\cdot1,2\cdot(-1,2)+(-1,2)^2$$

   $$=1,44-2,88+1,44=0.$$

3. $$a^2-b^2+a+b=(a^2-b^2)+(a+b)=(a-b)(a+b)+(a+b)$$

   $$=(a+b)(a-b+1).$$

4. $$a^2-b^2-a-b=(a^2-b^2)-(a+b)=(a-b)(a+b)-(a+b)$$

   $$=(a+b)(a-b-1).$$

5. $$x-y-x^2+y^2=(x-y)-(x^2-y^2)$$

   $$=(x-y)-(x-y)(x+y)$$

   $$=(x-y)(1-x-y).$$

6. $$x^3+x^2-x-1=x^2(x+1)-(x+1)$$

   $$=(x+1)(x^2-1)=(x+1)(x-1)(x+1)$$

   $$=(x+1)^2(x-1).$$

7. $$m^5-m^3+m^2-1=m^3(m^2-1)+(m^2-1)$$

   $$=(m^2-1)(m^3+1)=(m-1)(m+1)(m+1)(m^2-m+1)$$

   $$=(m+1)^2(m-1)(m^2-m+1).$$

8. $$x^4-x^3+x-1=x^3(x-1)+(x-1)$$

   $$=(x-1)(x^3+1)=(x-1)(x+1)(x^2-x+1).$$

Ответ

1. $$2$$
2. $$0$$
3. $$\left(a+b\right)\left(a-b+1\right)$$
4. $$\left(a+b\right)\left(a-b-1\right)$$
5. $$\left(x-y\right)\left(1-x-y\right)$$
6. $$\left(x+1\right)^2\left(x-1\right)$$
7. $$\left(m+1\right)^2\left(m-1\right)\left(m^2-m+1\right)$$
8. $$\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)$$