Solve left(2x-3right)^2-(5x+3)*(3-5x)-(2-4x)*(4+2x)

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

Evaluate

$$37x^{2}-8$$

Solution Steps

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

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

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.

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

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

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

Calculate 5 to the power of 2 and get 25.

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

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

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

Subtract 9 from 9 to get 0.

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

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

$$29x^{2}-12x-\left(2-4x\right)\left(4+2x\right)$$

Use the distributive property to multiply 2-4x by 4+2x and combine like terms.

$$29x^{2}-12x-\left(8-12x-8x^{2}\right)$$

To find the opposite of 8-12x-8x^{2}, find the opposite of each term.

$$29x^{2}-12x-8+12x+8x^{2}$$

Combine -12x and 12x to get 0.

$$29x^{2}-8+8x^{2}$$

Combine 29x^{2} and 8x^{2} to get 37x^{2}.

$$37x^{2}-8$$

Expand

$$37x^{2}-8$$

Solution Steps

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

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

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.

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

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

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

Calculate 5 to the power of 2 and get 25.

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

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

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

Subtract 9 from 9 to get 0.

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

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

$$29x^{2}-12x-\left(2-4x\right)\left(4+2x\right)$$

Use the distributive property to multiply 2-4x by 4+2x and combine like terms.

$$29x^{2}-12x-\left(8-12x-8x^{2}\right)$$

To find the opposite of 8-12x-8x^{2}, find the opposite of each term.

$$29x^{2}-12x-8+12x+8x^{2}$$

Combine -12x and 12x to get 0.

$$29x^{2}-8+8x^{2}$$

Combine 29x^{2} and 8x^{2} to get 37x^{2}.

$$37x^{2}-8$$