Упр.377 ГДЗ Муравин 7 класс (Алгебра)

1) (-0,8а + 50b)^2; 5) (9k^4 — 4n^3)^2;
2) (-2n^2- 0,1k)^2; 6) (0,6bc — 5b)^2;
3) (а + x)(а — х); 7) (0,4p^3 + 0,5pq^2)^2;
4) (-1,2p + 5/6 q); 8) (1/4 x^3 + 2y^2)^2;
9) (5/7 c^2 d — 9)(9 + 5/7 c^2 d);
10) (0,2с^2 — n^3)(0,2с^2 + n^3);
11) (-0,9аb — 0,2а^2 b^3)^2;
12) (15а^2 — 0,1b)(0,1b + 15а^2).

1. $$(-0,8a+50b)^2=(-0,8a)^2+2\cdot(-0,8a)\cdot 50b+(50b)^2$$
   $$=0,64a^2-80ab+2500b^2.$$
2. $$(-2n^2-0,1k)^2=(-2n^2)^2+2\cdot(-2n^2)\cdot(-0,1k)+(0,1k)^2$$
   $$=4n^4+0,4n^2k+0,01k^2.$$
3. $$(a+x)(a-x)=a^2-x^2.$$
4. $$\left(-1,2p+\frac56q\right)^2=\left(-1,2p\right)^2+2\cdot(-1,2p)\cdot\frac56q+\left(\frac56q\right)^2$$
   $$=1,44p^2-2pq+\frac{25}{36}q^2.$$
5. $$(9k^4-4n^3)^2=(9k^4)^2+2\cdot 9k^4\cdot(-4n^3)+(-4n^3)^2$$
   $$=81k^8-72k^4n^3+16n^6.$$
6. $$(0,6bc-5b)^2=(0,6bc)^2-2\cdot 0,6bc\cdot 5b+(5b)^2$$
   $$=0,36b^2c^2-6b^2c+25b^2.$$
7. $$(0,4p^3+0,5pq^2)^2=(0,4p^3)^2+2\cdot 0,4p^3\cdot 0,5pq^2+(0,5pq^2)^2$$
   $$=0,16p^6+0,4p^4q^2+0,25p^2q^4.$$
8. $$\left(\frac14x^3+2y^2\right)^2=\left(\frac14x^3\right)^2+2\cdot\frac14x^3\cdot 2y^2+(2y^2)^2$$
   $$=\frac1{16}x^6+x^3y^2+4y^4.$$
9. $$\left(\frac57c^2d-9\right)\left(9+\frac57c^2d\right)=\left(\frac57c^2d-9\right)\left(\frac57c^2d+9\right)$$
   $$=\left(\frac57c^2d\right)^2-9^2=\frac{25}{49}c^4d^2-81.$$
10. $$(0,2c^2-n^3)(0,2c^2+n^3)=(0,2c^2)^2-(n^3)^2$$
    $$=0,04c^4-n^6.$$
11. $$(-0,9ab-0,2a^2b^3)^2=(-0,9ab)^2+2\cdot(-0,9ab)\cdot(-0,2a^2b^3)+(0,2a^2b^3)^2$$
    $$=0,81a^2b^2+0,36a^3b^4+0,04a^4b^6.$$
12. $$(15a^2-0,1b)(0,1b+15a^2)=(15a^2-0,1b)(15a^2+0,1b)$$
    $$=(15a^2)^2-(0,1b)^2=225a^4-0,01b^2.$$

Ответ

1. $$0,64a^2-80ab+2500b^2$$
2. $$4n^4+0,4n^2k+0,01k^2$$
3. $$a^2-x^2$$
4. $$1,44p^2-2pq+\frac{25}{36}q^2$$
5. $$81k^8-72k^4n^3+16n^6$$
6. $$0,36b^2c^2-6b^2c+25b^2$$
7. $$0,16p^6+0,4p^4q^2+0,25p^2q^4$$
8. $$\frac1{16}x^6+x^3y^2+4y^4$$
9. $$\frac{25}{49}c^4d^2-81$$
10. $$0,04c^4-n^6$$
11. $$0,81a^2b^2+0,36a^3b^4+0,04a^4b^6$$
12. $$225a^4-0,01b^2$$