Алгебра 7 класс 1 Задание: Выполнить задание по образцу

Объяснение:

№2

х²+2ху+у²–49=(х+у)²–7²=(х+у+7)(х+у–7)

(х+у)²–7²=(х+у–7)(х+у+7)

(х+у–7)(х+у+7)=(х+у)²–7²=(х+у)²–49

№1

1) а²–2аb+b²–25= (a–b)²–5²= (a–b–5)(a–b+5)

2) x²–16b²+8bc–c²=x²–(4b–c²)²=(x–(4b–c))(x+4b–c)=(x–4b+c)(x+4b–c)

3) a³x²–ax–4a³–2a=a(a²x²–x–4a²–2)=a(a²(x²–4)–(x+2))= a(a²(x–2)(x+2)–(x+2))= a((x+2)(a²(x–2)–1)= a(x+2)(a²x–2a–1)

4) a³–27+a²–3a= (a–3)(a²+3a+9)+a(a–3)= (a–3)(a²+3a+9+a)=(a–3)(a²+4a–9)

5)(b^10)–25(b^8)–40b⁴–16= (b^8)(b²–25)–4(10b⁴–4)=(b+5)(b–5)–4(10b⁴–4)

6)8a³–27b³+4a²–12ab+9b²=(2a–3b)(4a²+6ab+9b²)+(2a–3b)²= (2a–3b)(4a²+6ab+9b+2a–3b)= (2a–3b)(4a²+6ab+6b+2a)=2*(2a–3b)(2a²+3ab+3b+a)

7) 4x²–12xy+9y²–4a²+4ab–b²= (2x–3y)²–(2a–b)²=(2x–3y–2a+b)(2x–3y+2a–b)

8) x²–y²–6x+9= (x–3)²–y²=(x–3–y)(x–3+y)

9) (x–y)(x+y)+2(2x–y)+3= x²–y²+4x–2y+3=x(x+4)–y(y+2)+3

5 и 9 не получается никак. Может опечатка.