(3a+2b)(3a-2b)-4(3a+2b)-এর সমাধান করুন

$$( 3 a + 2 b ) ( 3 a - 2 b ) - 4 ( 3 a + 2 b )$$

Evaluate

$$\left(3a-2b-4\right)\left(3a+2b\right)$$

Solution Steps

Consider \left(3a+2b\right)\left(3a-2b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3a\right)^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Expand \left(3a\right)^{2}.

$$3^{2}a^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Calculate 3 to the power of 2 and get 9.

$$9a^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Expand \left(2b\right)^{2}.

$$9a^{2}-2^{2}b^{2}-4\left(3a+2b\right)$$

Calculate 2 to the power of 2 and get 4.

$$9a^{2}-4b^{2}-4\left(3a+2b\right)$$

Use the distributive property to multiply -4 by 3a+2b.

$$9a^{2}-4b^{2}-12a-8b$$

Expand

$$9a^{2}-12a-4b^{2}-8b$$

Solution Steps

Consider \left(3a+2b\right)\left(3a-2b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3a\right)^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Expand \left(3a\right)^{2}.

$$3^{2}a^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Calculate 3 to the power of 2 and get 9.

$$9a^{2}-\left(2b\right)^{2}-4\left(3a+2b\right)$$

Expand \left(2b\right)^{2}.

$$9a^{2}-2^{2}b^{2}-4\left(3a+2b\right)$$

Calculate 2 to the power of 2 and get 4.

$$9a^{2}-4b^{2}-4\left(3a+2b\right)$$

Use the distributive property to multiply -4 by 3a+2b.

$$9a^{2}-4b^{2}-12a-8b$$