Упр.438 ГДЗ Никольский Потапов 7 класс (Алгебра)
7.
- а) $$\left(5-a\right)\left(3-a\right)-\left(a-4\right)^2$$;
- б) $$\left(x+3\right)^2+3\left(x-2\right)^2$$;
- в) $$3\left(2-m\right)^2+2\left(2-m\right)^2$$;
- г) $$5\left(2p-3\right)^2+2\left(5-2p\right)^2$$;
- д) $$4\left(3-5a\right)^2-5\left(a-3\right)\left(2a-3\right)$$;
- е) $$\left(a+1\right)^2+2\left(a+1\right)-3\left(a-1\right)\left(a+1\right)$$;
- ж) $$3-2\left(5-x\right)\left(x-5\right)-2\left(5+x\right)^2$$;
- з) $$\left(x-y-2\right)\left(x-y-z\right)-\left(x-y\right)^2$$;
- и) $$\left(x+y+z\right)\left(x-y-z\right)-\left(x+y-z\right)\left(x-y+z\right)$$;
- к) $$\left(x+y-z\right)\left(x-y+z\right)-\left(x+y+z\right)\left(x-y-z\right)$$.
а) $$(5-a)(3-a)-(a-4)^2=15-5a-3a+a^2-(a^2-8a+16)=-1$$
б) $$(x+3)^2+3(x-2)^2=x^2+6x+9+3(x^2-4x+4)=4x^2-6x+21$$
в) $$3(2-m)^2+2(2-m)^2=5(2-m)^2=5(4-4m+m^2)=20-20m+5m^2$$
г) $$5(2p-3)^2+2(5-2p)^2=5(4p^2-12p+9)+2(25-20p+4p^2)=28p^2-100p+95$$
д) $$4(3-5a)^2-5(a-3)(2a-3)=4(9-30a+25a^2)-5(2a^2-9a+9)=90a^2-75a-9$$
е) $$(a+1)^2+2(a+1)-3(a-1)(a+1)=(a+1)(a+1+2-3(a-1))=(a+1)(6-2a)=-2a^2+4a+6$$
ж) $$3-2(5-x)(x-5)-2(5+x)^2=3+2(5-x)^2-2(5+x)^2=3-40x$$
з) $$(x-y-z)(x-y-z)-(x-y)^2=(x-y-z)^2-(x-y)^2$$
$$=(x-y-z-(x-y))(x-y-z+(x-y))=(-z)(2x-2y-z)=z^2-2xz+2yz$$
и) $$(x+y+z)(x-y-z)-(x+y-z)(x-y+z)$$
$$=\bigl(x^2-(y+z)^2\bigr)-\bigl(x^2-(y-z)^2\bigr)=-4yz$$
к) $$(x+y-z)(x-y+z)-(x+y+z)(x-y-z)$$
$$=\bigl(x^2-(y-z)^2\bigr)-\bigl(x^2-(y+z)^2\bigr)=4yz$$
Ответ
а) $$-1$$; б) $$4x^2-6x+21$$; в) $$20-20m+5m^2$$; г) $$28p^2-100p+95$$; д) $$90a^2-75a-9$$; е) $$-2a^2+4a+6$$; ж) $$3-40x$$; з) $$z^2-2xz+2yz$$; и) $$-4yz$$; к) $$4yz$$.
