Упр.127 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (x-4)^2; 9) (y^2-2y)^2;
2) (5-x)^2; 10) (m^3+n^2 )^2;
3) (0,5a-b)^2; 11) (-7x+3y^3 )^2;
4) (3x-2)^2; 12) (-5-2a)^2;
5) (5m+3n)^2; 13) (2 1/4 a+1 2/3 b)^2;
6) (0,4a-5b)^2; 14) (6pq^2-qp^2 )^2;
7) (8x+1/2 y)^2; 15) (2x^4+5x^3 b^5 )^2.
8) (b^2-3)^2;

1. $$\left(x-4\right)^2=x^2-2\cdot x\cdot 4+4^2=x^2-8x+16.$$
2. $$\left(5-x\right)^2=5^2-2\cdot 5\cdot x+x^2=25-10x+x^2.$$
3. $$\left(0{,}5a-b\right)^2=\left(0{,}5a\right)^2-2\cdot 0{,}5a\cdot b+b^2=0{,}25a^2-ab+b^2.$$
4. $$\left(3x-2\right)^2=\left(3x\right)^2-2\cdot 3x\cdot 2+2^2=9x^2-12x+4.$$
5. $$\left(5m+3n\right)^2=\left(5m\right)^2+2\cdot 5m\cdot 3n+\left(3n\right)^2=25m^2+30mn+9n^2.$$
6. $$\left(0{,}4a-5b\right)^2=\left(0{,}4a\right)^2-2\cdot 0{,}4a\cdot 5b+\left(5b\right)^2=0{,}16a^2-4ab+25b^2.$$
7. $$\left(8x+\frac12 y\right)^2=\left(8x\right)^2+2\cdot 8x\cdot \frac12 y+\left(\frac12 y\right)^2=64x^2+8xy+\frac14 y^2.$$
8. $$\left(b^2-3\right)^2=\left(b^2\right)^2-2\cdot b^2\cdot 3+3^2=b^4-6b^2+9.$$
9. $$\left(y^2-2y\right)^2=\left(y^2\right)^2-2\cdot y^2\cdot 2y+\left(2y\right)^2=y^4-4y^3+4y^2.$$
10. $$\left(m^3+n^2\right)^2=\left(m^3\right)^2+2\cdot m^3\cdot n^2+\left(n^2\right)^2=m^6+2m^3n^2+n^4.$$
11. $$\left(-7x+3y^3\right)^2=\left(-7x\right)^2+2\cdot \left(-7x\right)\cdot 3y^3+\left(3y^3\right)^2=49x^2-42xy^3+9y^6.$$
12. $$\left(-5-2a\right)^2=\left(5+2a\right)^2=25+20a+4a^2.$$
13. $$\left(2\frac14 a+1\frac23 b\right)^2=\left(\frac94 a+\frac53 b\right)^2$$
    $$
    =\left(\frac94 a\right)^2+2\cdot \frac94 a\cdot \frac53 b+\left(\frac53 b\right)^2
    =\frac{81}{16}a^2+\frac{15}{2}ab+\frac{25}{9}b^2.
    $$
14. $$\left(6pq^2-qp^2\right)^2=\left(6pq^2\right)^2-2\cdot 6pq^2\cdot qp^2+\left(qp^2\right)^2$$
    $$=36p^2q^4-12p^3q^3+p^4q^2.$$
15. $$\left(2x^4+5x^3b^5\right)^2=\left(2x^4\right)^2+2\cdot 2x^4\cdot 5x^3b^5+\left(5x^3b^5\right)^2$$
    $$=4x^8+20x^7b^5+25x^6b^{10}.$$

Ответ

1) $$x^2-8x+16$$; 2) $$x^2-10x+25$$; 3) $$0{,}25a^2-ab+b^2$$; 4) $$9x^2-12x+4$$; 5) $$25m^2+30mn+9n^2$$; 6) $$0{,}16a^2-4ab+25b^2$$; 7) $$64x^2+8xy+\frac14 y^2$$; 8) $$b^4-6b^2+9$$; 9) $$y^4-4y^3+4y^2$$; 10) $$m^6+2m^3n^2+n^4$$; 11) $$49x^2-42xy^3+9y^6$$; 12) $$4a^2+20a+25$$; 13) $$\frac{81}{16}a^2+\frac{15}{2}ab+\frac{25}{9}b^2$$; 14) $$36p^2q^4-12p^3q^3+p^4q^2$$; 15) $$4x^8+20x^7b^5+25x^6b^{10}$$.