Solve (2x-3)^2-(5x+3)(3-5x)

$$( 2 x - 3 ) ^ { 2 } - ( 5 x + 3 ) ( 3 - 5 x )$$

Evaluate

$$x\left(29x-12\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9-\left(5x+3\right)\left(3-5x\right)$$

Consider \left(5x+3\right)\left(3-5x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-12x+9-\left(9-\left(5x\right)^{2}\right)$$

Expand \left(5x\right)^{2}.

$$4x^{2}-12x+9-\left(9-5^{2}x^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$4x^{2}-12x+9-\left(9-25x^{2}\right)$$

To find the opposite of 9-25x^{2}, find the opposite of each term.

$$4x^{2}-12x+9-9+25x^{2}$$

Subtract 9 from 9 to get 0.

$$4x^{2}-12x+25x^{2}$$

Combine 4x^{2} and 25x^{2} to get 29x^{2}.

$$29x^{2}-12x$$

Expand

$$29x^{2}-12x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9-\left(5x+3\right)\left(3-5x\right)$$

Consider \left(5x+3\right)\left(3-5x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-12x+9-\left(9-\left(5x\right)^{2}\right)$$

Expand \left(5x\right)^{2}.

$$4x^{2}-12x+9-\left(9-5^{2}x^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$4x^{2}-12x+9-\left(9-25x^{2}\right)$$

To find the opposite of 9-25x^{2}, find the opposite of each term.

$$4x^{2}-12x+9-9+25x^{2}$$

Subtract 9 from 9 to get 0.

$$4x^{2}-12x+25x^{2}$$

Combine 4x^{2} and 25x^{2} to get 29x^{2}.

$$29x^{2}-12x$$