Упр.295 ГДЗ Никольский Потапов 7 класс (Алгебра)

а) $$\left(5m+7n\right)\left(2n+4m\right)$$; б) $$\left(12a+b\right)\left(3a+5b\right)$$; в) $$\left(2x-3y\right)\left(2x+3y\right)$$; г) $$\left(5m-2n\right)\left(3n-m\right)$$; д) $$\left(-a-b\right)\left(2a-3b\right)$$; е) $$\left(-7x-4y\right)\left(-5x+7y\right)$$; ж) $$\left(a^2+b^2\right)\left(a^2+b^2\right)$$; з) $$\left(mn^3-m^2\right)\left(m-1\right)$$; и) $$\left(2x^2-y^2\right)\left(y^2+2x^3\right)$$; к) $$\left(xy^2+3a^2\right)\left(3xy+a^3\right)$$.

1. $$\begin{aligned} (5m+7n)(2n+4m)&=5m\cdot 2n+5m\cdot 4m+7n\cdot 2n+7n\cdot 4m\\ &=10mn+20m^2+14n^2+28mn\\ &=20m^2+38mn+14n^2. \end{aligned}$$
2. $$\begin{aligned} (12a+b)(3a+5b)&=12a\cdot 3a+12a\cdot 5b+b\cdot 3a+b\cdot 5b\\ &=36a^2+60ab+3ab+5b^2\\ &=36a^2+63ab+5b^2. \end{aligned}$$
3. $$\begin{aligned} (2x-3y)(2x+3y)&=(2x)^2-(3y)^2\\ &=4x^2-9y^2. \end{aligned}$$
4. $$\begin{aligned} (5m-2n)(3n-5m)&=5m\cdot 3n+5m\cdot(-5m)-2n\cdot 3n-2n\cdot(-5m)\\ &=15mn-25m^2-6n^2+10mn\\ &=-25m^2+25mn-6n^2. \end{aligned}$$
5. $$\begin{aligned} (-a-b)(2a-3b)&=-a\cdot 2a+(-a)\cdot(-3b)-b\cdot 2a-b\cdot(-3b)\\ &=-2a^2+3ab-2ab+3b^2\\ &=-2a^2+ab+3b^2. \end{aligned}$$
6. $$\begin{aligned} (-7x-4y)(-5x+7y)&=35x^2-49xy+20xy-28y^2\\ &=35x^2-29xy-28y^2. \end{aligned}$$
7. $$\begin{aligned} (a^2+b^2)(a^2+b^2)&=a^4+a^2b^2+a^2b^2+b^4\\ &=a^4+2a^2b^2+b^4. \end{aligned}$$
8. $$\begin{aligned} (mn^3-m^2)(m-1)&=mn^3\cdot m-mn^3\cdot 1-m^2\cdot m+m^2\cdot 1\\ &=m^2n^3-mn^3-m^3+m^2. \end{aligned}$$
9. $$\begin{aligned} (2x^2-y^2)(y^2+2x^3)&=2x^2\cdot y^2+2x^2\cdot 2x^3-y^2\cdot y^2-y^2\cdot 2x^3\\ &=2x^2y^2+4x^5-y^4-2x^3y^2. \end{aligned}$$
10. $$\begin{aligned} (xy^2+3a^2)(3xy+a^3)&=xy^2\cdot 3xy+xy^2\cdot a^3+3a^2\cdot 3xy+3a^2\cdot a^3\\ &=3x^2y^3+a^3xy^2+9a^2xy+3a^5. \end{aligned}$$

Ответ

а) $$20m^2+38mn+14n^2$$;
б) $$36a^2+63ab+5b^2$$;
в) $$4x^2-9y^2$$;
г) $$-25m^2+25mn-6n^2$$;
д) $$-2a^2+ab+3b^2$$;
е) $$35x^2-29xy-28y^2$$;
ж) $$a^4+2a^2b^2+b^4$$;
з) $$m^2n^3-mn^3-m^3+m^2$$;
и) $$2x^2y^2+4x^5-y^4-2x^3y^2$$;
к) $$3x^2y^3+a^3xy^2+9a^2xy+3a^5$$.