Solve (2x+3)(2x-3)-4(x+9)(x-1/4)

$$( 2 x + 3 ) ( 2 x - 3 ) - 4 ( x + 9 ) ( x - \frac { 1 } { 4 } )$$

Evaluate

$$-35x$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

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

Use the distributive property to multiply -4 by x+9.

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

Apply the distributive property by multiplying each term of -4x-36 by each term of x-\frac{1}{4}.

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

Multiply -4 times -\frac{1}{4}.

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

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

$$4x^{2}-9-4x^{2}-35x-36\left(-\frac{1}{4}\right)$$

Express -36\left(-\frac{1}{4}\right) as a single fraction.

$$4x^{2}-9-4x^{2}-35x+\frac{-36\left(-1\right)}{4}$$

Multiply -36 and -1 to get 36.

$$4x^{2}-9-4x^{2}-35x+\frac{36}{4}$$

Divide 36 by 4 to get 9.

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

Combine 4x^{2} and -4x^{2} to get 0.

$$-9-35x+9$$

Add -9 and 9 to get 0.

$$-35x$$

Expand

$$-35x$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

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

Use the distributive property to multiply -4 by x+9.

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

Apply the distributive property by multiplying each term of -4x-36 by each term of x-\frac{1}{4}.

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

Multiply -4 times -\frac{1}{4}.

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

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

$$4x^{2}-9-4x^{2}-35x-36\left(-\frac{1}{4}\right)$$

Express -36\left(-\frac{1}{4}\right) as a single fraction.

$$4x^{2}-9-4x^{2}-35x+\frac{-36\left(-1\right)}{4}$$

Multiply -36 and -1 to get 36.

$$4x^{2}-9-4x^{2}-35x+\frac{36}{4}$$

Divide 36 by 4 to get 9.

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

Combine 4x^{2} and -4x^{2} to get 0.

$$-9-35x+9$$

Add -9 and 9 to get 0.

$$-35x$$