Упр.409 ГДЗ Муравин 7 класс (Алгебра)

1) 20а^2 b — 45by^2; 4) 144b^4 — 81b^2 с^4;
2) 0,64р^5 — 0,36p^3 q^2; 5) 108х^7 у^5 — 4800х^3 у^3;
3) 0,3х^3 у — 2,7ху^3; 6) 1200а^3 b^4 с^5 — 147аb^2 с.

1. $$20a^2b-45by^2=5b(4a^2-9y^2)=5b(2a-3y)(2a+3y)$$
2. $$0{,}64p^5-0{,}36p^3q^2=p^3(0{,}64p^2-0{,}36q^2)=p^3(0{,}8p-0{,}6q)(0{,}8p+0{,}6q)$$
3. $$0{,}3x^3y-2{,}7xy^3=0{,}3xy(x^2-9y^2)=0{,}3xy(x-3y)(x+3y)$$
4. $$144b^4-81b^2c^4=9b^2(16b^2-9c^4)=9b^2(4b-3c^2)(4b+3c^2)$$
5. $$108x^7y^5-4800x^3y^3=12x^3y^3(9x^4y^2-400)=12x^3y^3(3x^2y-20)(3x^2y+20)$$
6. $$1200a^3b^4c^5-147ab^2c=3ab^2c(400a^2b^2c^4-49)=3ab^2c(20abc^2-7)(20abc^2+7)$$

Ответ

1) $$5b(2a-3y)(2a+3y)$$
2) $$p^3(0{,}8p-0{,}6q)(0{,}8p+0{,}6q)$$
3) $$0{,}3xy(x-3y)(x+3y)$$
4) $$9b^2(4b-3c^2)(4b+3c^2)$$
5) $$12x^3y^3(3x^2y-20)(3x^2y+20)$$
6) $$3ab^2c(20abc^2-7)(20abc^2+7)$$