Упр.410 ГДЗ Муравин 7 класс (Алгебра)

1) 20x^3 — 140х^2 у + 245ху^2;
2) 100k^4 — 120k^3 n + 36k^2 n^2;
3) (3а + 4)^2 — (а — 12)^2;
4) (5x — 7)^2 — (5 — 3x)^2;
5) (а^2 + баb + 16b^2)^2 — (баb + 20b^2)^2;
6) (4 — 6у^3 + 4у^6)^2 — (6у^3 — 5у^6)^2.

1. $$20x^3-140x^2y+245xy^2=5x(4x^2-28xy+49y^2)=5x(2x-7y)^2.$$
2. $$100k^4-120k^3n+36k^2n^2=k^2(100k^2-120kn+36n^2)=k^2(10k-6n)^2=4k^2(5k-3n)^2.$$
3. $$ (3a+4)^2-(a-12)^2=((3a+4)-(a-12))((3a+4)+(a-12)) $$
   $$ =(2a+16)(4a-8)=2(a+8)\cdot 4(a-2)=8(a+8)(a-2). $$
4. $$ (5x-7)^2-(5-3x)^2=((5x-7)-(5-3x))((5x-7)+(5-3x)) $$
   $$ =(8x-12)(2x-2)=4(2x-3)\cdot 2(x-1)=8(2x-3)(x-1). $$
5. $$ (a^2+6ab+16b^2)^2-(6ab+20b^2)^2 $$
   $$ =\bigl((a^2+6ab+16b^2)-(6ab+20b^2)\bigr)\bigl((a^2+6ab+16b^2)+(6ab+20b^2)\bigr) $$
   $$ =(a^2-4b^2)(a^2+12ab+36b^2) =(a-2b)(a+2b)(a+6b)^2. $$
6. $$ (4-6y^3+4y^6)^2-(6y^3-5y^6)^2 $$
   $$ =\bigl((4-6y^3+4y^6)-(6y^3-5y^6)\bigr)\bigl((4-6y^3+4y^6)+(6y^3-5y^6)\bigr) $$
   $$ =(4-12y^3+9y^6)(4-y^6)=(2-3y^3)^2(2-y^3)(2+y^3). $$

Ответ

1) $$5x(2x-7y)^2$$
2) $$4k^2(5k-3n)^2$$
3) $$8(a+8)(a-2)$$
4) $$8(2x-3)(x-1)$$
5) $$ (a-2b)(a+2b)(a+6b)^2 $$
6) $$ (2-3y^3)^2(2-y^3)(2+y^3) $$