Solve (3x-4)^2+(3x+4)^2-2(3x-4)(3x+4)

$$( 3 x - 4 ) ^ { 2 } + ( 3 x + 4 ) ^ { 2 } - 2 ( 3 x - 4 ) ( 3 x + 4 )$$

Evaluate

$$64$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$9x^{2}-24x+16+\left(3x+4\right)^{2}-2\left(3x-4\right)\left(3x+4\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4\right)^{2}.

$$9x^{2}-24x+16+9x^{2}+24x+16-2\left(3x-4\right)\left(3x+4\right)$$

Combine 9x^{2} and 9x^{2} to get 18x^{2}.

$$18x^{2}-24x+16+24x+16-2\left(3x-4\right)\left(3x+4\right)$$

Combine -24x and 24x to get 0.

$$18x^{2}+16+16-2\left(3x-4\right)\left(3x+4\right)$$

Add 16 and 16 to get 32.

$$18x^{2}+32-2\left(3x-4\right)\left(3x+4\right)$$

Use the distributive property to multiply -2 by 3x-4.

$$18x^{2}+32+\left(-6x+8\right)\left(3x+4\right)$$

Use the distributive property to multiply -6x+8 by 3x+4 and combine like terms.

$$18x^{2}+32-18x^{2}+32$$

Combine 18x^{2} and -18x^{2} to get 0.

$$32+32$$

Add 32 and 32 to get 64.

$$64$$

Factor

$$2^{6}$$