Упр.16.8 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x+2)^2-49; 6) (8y+4)^2-(4y-3)^2;
2) (x-10)^2-25y^2; 7) (5a+3b)^2-(2a-4b)^2;
3) 25-(y-3)^2; 8) 4(a-b)^2-(a+b)^2;
4) (a-4)^2-(a+2)^2; 9) (x^2+x+1)^2-(x^2-x+2)^2;
5) (m-10)^2-(n-6)^2; 10) (-3x^3+y)^2-16x^6.

1. $$\begin{aligned} (x+2)^2-49&=(x+2)^2-7^2\\ &=(x+2-7)(x+2+7)\\ &=(x-5)(x+9). \end{aligned}$$
2. $$\begin{aligned} (x-10)^2-25y^2&=(x-10)^2-(5y)^2\\ &=(x-10-5y)(x-10+5y). \end{aligned}$$
3. $$\begin{aligned} 25-(y-3)^2&=5^2-(y-3)^2\\ &=(5-(y-3))(5+(y-3))\\ &=(8-y)(y+2). \end{aligned}$$
4. $$\begin{aligned} (a-4)^2-(a+2)^2&=\bigl((a-4)-(a+2)\bigr)\bigl((a-4)+(a+2)\bigr)\\ &=(-6)(2a-2)\\ &=-12(a-1). \end{aligned}$$
5. $$\begin{aligned} (m-10)^2-(n-6)^2&=\bigl((m-10)-(n-6)\bigr)\bigl((m-10)+(n-6)\bigr)\\ &=(m-n-4)(m+n-16). \end{aligned}$$
6. $$\begin{aligned} (8y+4)^2-(4y-3)^2&=\bigl((8y+4)-(4y-3)\bigr)\bigl((8y+4)+(4y-3)\bigr)\\ &=(4y+7)(12y+1). \end{aligned}$$
7. $$\begin{aligned} (5a+3b)^2-(2a-4b)^2&=\bigl((5a+3b)-(2a-4b)\bigr)\bigl((5a+3b)+(2a-4b)\bigr)\\ &=(3a+7b)(7a-b). \end{aligned}$$
8. $$\begin{aligned} 4(a-b)^2-(a+b)^2&=\bigl(2(a-b)-(a+b)\bigr)\bigl(2(a-b)+(a+b)\bigr)\\ &=(a-3b)(3a-b). \end{aligned}$$
9. $$\begin{aligned} (x^2+x+1)^2-(x^2-x+2)^2&=\bigl((x^2+x+1)-(x^2-x+2)\bigr)\bigl((x^2+x+1)+(x^2-x+2)\bigr)\\ &=(2x-1)(2x^2+3). \end{aligned}$$
10. $$\begin{aligned} (-3x^3+y)^2-16x^6&=(-3x^3+y)^2-(4x^3)^2\\ &\bigl((-3x^3+y)-4x^3\bigr)\bigl((-3x^3+y)+4x^3\bigr)\\ &=(y-7x^3)(y+x^3). \end{aligned}$$

Ответ

1) $$(x-5)(x+9)$$
2) $$(x-10-5y)(x-10+5y)$$
3) $$(8-y)(y+2)$$
4) $$-12(a-1)$$
5) $$(m-n-4)(m+n-16)$$
6) $$(4y+7)(12y+1)$$
7) $$(3a+7b)(7a-b)$$
8) $$(a-3b)(3a-b)$$
9) $$(2x-1)(2x^2+3)$$
10) $$(y-7x^3)(y+x^3)$$