Упр.376 ГДЗ Муравин 7 класс (Алгебра)

1) (5x + …)^2 = … + 70ху + …;
2) (9а — …)^2 = … — … + 100b^2;
3) 16b^2 — … = (… + 64а)(… — 64а);
4) (… + 10а)^2 = … — 60аn + …;
5) (с^2 — …)^2 = … — 24с^2 у + …;
6) … — 0,09у^2 = (… — 0,3y)(0,3y + 3z);
7) (… — …)^2 = 36а^2 — … + 49с^2;
8) (… + …)^2 = 25x^2 + 80ху + … .

1. $$70xy=2\cdot 5x\cdot 7y$$
   $$\left(5x+7y\right)^2=25x^2+70xy+49y^2$$
2. $$100b^2=\left(10b\right)^2$$
   $$\left(9a-10b\right)^2=81a^2-180ab+100b^2$$
3. $$16b^2=\left(4b\right)^2,\quad 4096a^2=\left(64a\right)^2$$
   $$16b^2-4096a^2=\left(4b+64a\right)\left(4b-64a\right)$$
4. $$-60an=2\cdot 10a\cdot(-3n)$$
   $$\left(-3n+10a\right)^2=\left(10a-3n\right)^2=100a^2-60an+9n^2$$
5. $$24c^2y=2\cdot c^2\cdot 12y$$
   $$\left(c^2-12y\right)^2=c^4-24c^2y+144y^2$$
6. $$9z^2=\left(3z\right)^2$$
   $$9z^2-0{,}09y^2=\left(3z-0{,}3y\right)\left(3z+0{,}3y\right)$$
7. $$36a^2=\left(6a\right)^2,\quad 49c^2=\left(7c\right)^2$$
   $$\left(6a-7c\right)^2=36a^2-84ac+49c^2$$
8. $$25x^2=\left(5x\right)^2,\quad 80xy=2\cdot 5x\cdot 8y$$
   $$\left(5x+8y\right)^2=25x^2+80xy+64y^2$$

Ответ

1) $$\left(5x+7y\right)^2=25x^2+70xy+49y^2$$
2) $$\left(9a-10b\right)^2=81a^2-180ab+100b^2$$
3) $$16b^2-4096a^2=\left(4b+64a\right)\left(4b-64a\right)$$
4) $$\left(-3n+10a\right)^2=100a^2-60an+9n^2$$
5) $$\left(c^2-12y\right)^2=c^4-24c^2y+144y^2$$
6) $$9z^2-0{,}09y^2=\left(3z-0{,}3y\right)\left(3z+0{,}3y\right)$$
7) $$\left(6a-7c\right)^2=36a^2-84ac+49c^2$$
8) $$\left(5x+8y\right)^2=25x^2+80xy+64y^2$$