Solve (3x-1)(3x+1)-(x-4)(9x+1)

$$( 3 x - 1 ) ( 3 x + 1 ) - ( x - 4 ) ( 9 x + 1 )$$

Evaluate

$$35x+3$$

Solution Steps

Consider \left(3x-1\right)\left(3x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3x\right)^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

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

$$3^{2}x^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

Calculate 1 to the power of 2 and get 1.

$$9x^{2}-1-\left(x-4\right)\left(9x+1\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of 9x+1.

$$9x^{2}-1-\left(9x^{2}+x-36x-4\right)$$

Combine x and -36x to get -35x.

$$9x^{2}-1-\left(9x^{2}-35x-4\right)$$

To find the opposite of 9x^{2}-35x-4, find the opposite of each term.

$$9x^{2}-1-9x^{2}-\left(-35x\right)-\left(-4\right)$$

The opposite of -35x is 35x.

$$9x^{2}-1-9x^{2}+35x-\left(-4\right)$$

The opposite of -4 is 4.

$$9x^{2}-1-9x^{2}+35x+4$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-1+35x+4$$

Add -1 and 4 to get 3.

$$3+35x$$

Expand

$$35x+3$$

Solution Steps

Consider \left(3x-1\right)\left(3x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3x\right)^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

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

$$3^{2}x^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}-1^{2}-\left(x-4\right)\left(9x+1\right)$$

Calculate 1 to the power of 2 and get 1.

$$9x^{2}-1-\left(x-4\right)\left(9x+1\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of 9x+1.

$$9x^{2}-1-\left(9x^{2}+x-36x-4\right)$$

Combine x and -36x to get -35x.

$$9x^{2}-1-\left(9x^{2}-35x-4\right)$$

To find the opposite of 9x^{2}-35x-4, find the opposite of each term.

$$9x^{2}-1-9x^{2}-\left(-35x\right)-\left(-4\right)$$

The opposite of -35x is 35x.

$$9x^{2}-1-9x^{2}+35x-\left(-4\right)$$

The opposite of -4 is 4.

$$9x^{2}-1-9x^{2}+35x+4$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-1+35x+4$$

Add -1 and 4 to get 3.

$$3+35x$$