Solve 3*(2-5x)-(4x-5)*(4x+5)

$$3 \cdot ( 2 - 5 x ) - ( 4 x - 5 ) \cdot ( 4 x + 5 )$$

Evaluate

$$\left(1-x\right)\left(16x+31\right)$$

Solution Steps

Use the distributive property to multiply 3 by 2-5x.

$$6-15x-\left(4x-5\right)\left(4x+5\right)$$

Consider \left(4x-5\right)\left(4x+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$6-15x-\left(\left(4x\right)^{2}-5^{2}\right)$$

Expand \left(4x\right)^{2}.

$$6-15x-\left(4^{2}x^{2}-5^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$6-15x-\left(16x^{2}-5^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$6-15x-\left(16x^{2}-25\right)$$

To find the opposite of 16x^{2}-25, find the opposite of each term.

$$6-15x-16x^{2}-\left(-25\right)$$

The opposite of -25 is 25.

$$6-15x-16x^{2}+25$$

Add 6 and 25 to get 31.

$$31-15x-16x^{2}$$

Expand

$$31-15x-16x^{2}$$

Solution Steps

Use the distributive property to multiply 3 by 2-5x.

$$6-15x-\left(4x-5\right)\left(4x+5\right)$$

Consider \left(4x-5\right)\left(4x+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$6-15x-\left(\left(4x\right)^{2}-5^{2}\right)$$

Expand \left(4x\right)^{2}.

$$6-15x-\left(4^{2}x^{2}-5^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$6-15x-\left(16x^{2}-5^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$6-15x-\left(16x^{2}-25\right)$$

To find the opposite of 16x^{2}-25, find the opposite of each term.

$$6-15x-16x^{2}-\left(-25\right)$$

The opposite of -25 is 25.

$$6-15x-16x^{2}+25$$

Add 6 and 25 to get 31.

$$31-15x-16x^{2}$$