(2x-y)^2-(x-5y)^2= eching

$$( 2 x - y ) ^ { 2 } - ( x - 5 y ) ^ { 2 } =$$

Baholash

$$3\left(x-2y\right)\left(x+4y\right)$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-y\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-4xy+y^{2}-\left(x-5y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-5y\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-4xy+y^{2}-\left(x^{2}-10xy+25y^{2}\right)$$

x^{2}-10xy+25y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-4xy+y^{2}-x^{2}+10xy-25y^{2}$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}-4xy+y^{2}+10xy-25y^{2}$$

6xy ni olish uchun -4xy va 10xy ni birlashtirish.

$$3x^{2}+6xy+y^{2}-25y^{2}$$

-24y^{2} ni olish uchun y^{2} va -25y^{2} ni birlashtirish.

$$3x^{2}+6xy-24y^{2}$$

Kengaytirish

$$3x^{2}+6xy-24y^{2}$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-y\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-4xy+y^{2}-\left(x-5y\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-5y\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-4xy+y^{2}-\left(x^{2}-10xy+25y^{2}\right)$$

x^{2}-10xy+25y^{2} teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-4xy+y^{2}-x^{2}+10xy-25y^{2}$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}-4xy+y^{2}+10xy-25y^{2}$$

6xy ni olish uchun -4xy va 10xy ni birlashtirish.

$$3x^{2}+6xy+y^{2}-25y^{2}$$

-24y^{2} ni olish uchun y^{2} va -25y^{2} ni birlashtirish.

$$3x^{2}+6xy-24y^{2}$$