Упр.409 ГДЗ Муравин 7 класс (Алгебра)

1. Разложите на множители двучлен: 1) $$20а^2b-45by^2$$; 4) $$144b^4-81b^2с^4$$; 2) $$0{,}64р^5-0{,}36p^3q^2$$; 5) $$108х^7у^5-4800х^3у^3$$; 3) $$0{,}3х^3у-2{,}7ху^3$$; 6) $$1200а^3b^4с^5-147аb^2с$$.

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) $$3ab^2c(20abc^2-7)(20abc^2+7)$$