(a+3b)^2-(a-4b)^2= eching

$$( a + 3 b ) ^ { 2 } - ( a - 4 b ) ^ { 2 } =$$

Baholash

$$7b\left(2a-b\right)$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+3b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+6ab+9b^{2}-\left(a-4b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-4b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+6ab+9b^{2}-\left(a^{2}-8ab+16b^{2}\right)$$

a^{2}-8ab+16b^{2} teskarisini topish uchun har birining teskarisini toping.

$$a^{2}+6ab+9b^{2}-a^{2}+8ab-16b^{2}$$

0 ni olish uchun a^{2} va -a^{2} ni birlashtirish.

$$6ab+9b^{2}+8ab-16b^{2}$$

14ab ni olish uchun 6ab va 8ab ni birlashtirish.

$$14ab+9b^{2}-16b^{2}$$

-7b^{2} ni olish uchun 9b^{2} va -16b^{2} ni birlashtirish.

$$14ab-7b^{2}$$

Kengaytirish

$$14ab-7b^{2}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+3b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+6ab+9b^{2}-\left(a-4b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-4b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+6ab+9b^{2}-\left(a^{2}-8ab+16b^{2}\right)$$

a^{2}-8ab+16b^{2} teskarisini topish uchun har birining teskarisini toping.

$$a^{2}+6ab+9b^{2}-a^{2}+8ab-16b^{2}$$

0 ni olish uchun a^{2} va -a^{2} ni birlashtirish.

$$6ab+9b^{2}+8ab-16b^{2}$$

14ab ni olish uchun 6ab va 8ab ni birlashtirish.

$$14ab+9b^{2}-16b^{2}$$

-7b^{2} ni olish uchun 9b^{2} va -16b^{2} ni birlashtirish.

$$14ab-7b^{2}$$