Упр.560 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) 4x^8-81y^4; 2) 16a^6-25b^8; 3) (x+y)^2-z^2; 4) m^2-(n-k)^2;
4) 25x^4 y^6-(9/16)a^6 b^6; 6) (1/25)a^6 b^2-(4/49)c^8;
7) (x+y)^2-16(x-y)^2; 8) (a+b)^2+4(a+b)+4.

1. $$4x^8-81y^4=(2x^4)^2-(9y^2)^2=(2x^4-9y^2)(2x^4+9y^2)$$
   $$=(\sqrt{2}x^2-3y)(\sqrt{2}x^2+3y)(2x^4+9y^2)$$
2. $$16a^6-25b^8=(4a^3)^2-(5b^4)^2=(4a^3-5b^4)(4a^3+5b^4)$$
3. $$ (x+y)^2-z^2=((x+y)-z)((x+y)+z)=(x+y-z)(x+y+z) $$
4. $$m^2-(n-k)^2=(m-(n-k))(m+(n-k))=(m-n+k)(m+n-k)$$
5. $$25x^4y^6-\frac{9}{16}a^6b^6=(5x^2y^3)^2-\left(\frac{3}{4}a^3b^3\right)^2$$
   $$=\left(5x^2y^3-\frac{3}{4}a^3b^3\right)\left(5x^2y^3+\frac{3}{4}a^3b^3\right)$$
6. $$\frac{1}{25}a^6b^2-\frac{4}{49}c^8=\left(\frac{1}{5}a^3b\right)^2-\left(\frac{2}{7}c^4\right)^2$$
   $$=\left(\frac{1}{5}a^3b-\frac{2}{7}c^4\right)\left(\frac{1}{5}a^3b+\frac{2}{7}c^4\right)$$
7. $$(x+y)^2-16(x-y)^2=((x+y)-4(x-y))((x+y)+4(x-y))$$
   $$=(x+y-4x+4y)(x+y+4x-4y)=(5y-3x)(5x-3y)$$
8. $$(a+b)^2+4(a+b)+4=((a+b)+2)^2=(a+b+2)^2$$

Ответ

1) $$(\sqrt{2}x^2-3y)(\sqrt{2}x^2+3y)(2x^4+9y^2)$$
2) $$(4a^3-5b^4)(4a^3+5b^4)$$
3) $$(x+y-z)(x+y+z)$$
4) $$(m-n+k)(m+n-k)$$
5) $$\left(5x^2y^3-\frac{3}{4}a^3b^3\right)\left(5x^2y^3+\frac{3}{4}a^3b^3\right)$$
6) $$\left(\frac{1}{5}a^3b-\frac{2}{7}c^4\right)\left(\frac{1}{5}a^3b+\frac{2}{7}c^4\right)$$
7) $$(5y-3x)(5x-3y)$$
8) $$(a+b+2)^2$$