left(5x+2yright)^2-left(2x+5yright)^2 eching

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

Baholash

$$21\left(x^{2}-y^{2}\right)$$

Yechim qadamlari

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

$$25x^{2}+20xy+4y^{2}-\left(2x+5y\right)^{2}$$

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

$$25x^{2}+20xy+4y^{2}-\left(4x^{2}+20xy+25y^{2}\right)$$

4x^{2}+20xy+25y^{2} teskarisini topish uchun har birining teskarisini toping.

$$25x^{2}+20xy+4y^{2}-4x^{2}-20xy-25y^{2}$$

21x^{2} ni olish uchun 25x^{2} va -4x^{2} ni birlashtirish.

$$21x^{2}+20xy+4y^{2}-20xy-25y^{2}$$

0 ni olish uchun 20xy va -20xy ni birlashtirish.

$$21x^{2}+4y^{2}-25y^{2}$$

-21y^{2} ni olish uchun 4y^{2} va -25y^{2} ni birlashtirish.

$$21x^{2}-21y^{2}$$

Kengaytirish

$$21x^{2}-21y^{2}$$

Yechim qadamlari

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

$$25x^{2}+20xy+4y^{2}-\left(2x+5y\right)^{2}$$

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

$$25x^{2}+20xy+4y^{2}-\left(4x^{2}+20xy+25y^{2}\right)$$

4x^{2}+20xy+25y^{2} teskarisini topish uchun har birining teskarisini toping.

$$25x^{2}+20xy+4y^{2}-4x^{2}-20xy-25y^{2}$$

21x^{2} ni olish uchun 25x^{2} va -4x^{2} ni birlashtirish.

$$21x^{2}+20xy+4y^{2}-20xy-25y^{2}$$

0 ni olish uchun 20xy va -20xy ni birlashtirish.

$$21x^{2}+4y^{2}-25y^{2}$$

-21y^{2} ni olish uchun 4y^{2} va -25y^{2} ni birlashtirish.

$$21x^{2}-21y^{2}$$