Упр.699 ГДЗ Никольский Потапов 8 класс (Алгебра)

а) $$m^3-4m^2+20m-125$$; б) $$8-2p+3p^2-27p^3$$; в) $$(x^2+4x)^2-(x-9)^2$$; г) $$(9x^2+2)^2-(6x+7)^2$$; д) $$(5a-7b)^2-2(5a-7b)+1$$; е) $$1+2(x-3y)+(x-3y)^2$$.

1. а) $$m^3-4m^2+20m-125=(m^3-125)-4m(m-5)$$

   $$=(m-5)(m^2+5m+25)-4m(m-5)$$

   $$=(m-5)(m^2+5m+25-4m)=(m-5)(m^2+m+25).$$

2. б) $$8-2p+3p^2-27p^3=(8-27p^3)-p(2-3p)$$

   $$=(2-3p)(4+6p+9p^2)-p(2-3p)$$

   $$=(2-3p)(4+6p+9p^2-p)=(2-3p)(4+5p+9p^2).$$

3. в) $$\left(x^2+4x\right)^2-(x-9)^2$$

   $$=\left(x^2+4x-x+9\right)\left(x^2+4x+x-9\right)$$

   $$=(x^2+3x+9)(x^2+5x-9).$$

4. г) $$\left(9x^2+2\right)^2-(6x+7)^2$$

   $$=\left(9x^2+2-6x-7\right)\left(9x^2+2+6x+7\right)$$

   $$=(9x^2-6x-5)(9x^2+6x+9)$$

   $$=3(9x^2-6x-5)(3x^2+2x+3).$$

5. д) $$\left(5a-7b\right)^2-2\left(5a-7b\right)+1=\left(5a-7b-1\right)^2.$$

6. е) $$1+2(x-3y)+(x-3y)^2=\left(1+x-3y\right)^2.$$

Ответ

а) $$\left(m-5\right)\left(m^2+m+25\right);$$ б) $$\left(2-3p\right)\left(4+5p+9p^2\right);$$ в) $$\left(x^2+3x+9\right)\left(x^2+5x-9\right);$$ г) $$3\left(9x^2-6x-5\right)\left(3x^2+2x+3\right);$$ д) $$\left(5a-7b-1\right)^2;$$ е) $$\left(1+x-3y\right)^2.$$