Solve left(3x-7right)^2-4(3x-7)left(3x+7right)^2

$${ \left(3x-7 \right) }^{ 2 } -4(3x-7) { \left(3x+7 \right) }^{ 2 }$$

Evaluate

$$1421+546x-243x^{2}-108x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-7\right)^{2}.

$$9x^{2}-42x+49-4\left(3x-7\right)\left(3x+7\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+7\right)^{2}.

$$9x^{2}-42x+49-4\left(3x-7\right)\left(9x^{2}+42x+49\right)$$

Use the distributive property to multiply -4 by 3x-7.

$$9x^{2}-42x+49+\left(-12x+28\right)\left(9x^{2}+42x+49\right)$$

Use the distributive property to multiply -12x+28 by 9x^{2}+42x+49 and combine like terms.

$$9x^{2}-42x+49-108x^{3}-252x^{2}+588x+1372$$

Combine 9x^{2} and -252x^{2} to get -243x^{2}.

$$-243x^{2}-42x+49-108x^{3}+588x+1372$$

Combine -42x and 588x to get 546x.

$$-243x^{2}+546x+49-108x^{3}+1372$$

Add 49 and 1372 to get 1421.

$$-243x^{2}+546x+1421-108x^{3}$$

Expand

$$1421+546x-243x^{2}-108x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-7\right)^{2}.

$$9x^{2}-42x+49-4\left(3x-7\right)\left(3x+7\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+7\right)^{2}.

$$9x^{2}-42x+49-4\left(3x-7\right)\left(9x^{2}+42x+49\right)$$

Use the distributive property to multiply -4 by 3x-7.

$$9x^{2}-42x+49+\left(-12x+28\right)\left(9x^{2}+42x+49\right)$$

Use the distributive property to multiply -12x+28 by 9x^{2}+42x+49 and combine like terms.

$$9x^{2}-42x+49-108x^{3}-252x^{2}+588x+1372$$

Combine 9x^{2} and -252x^{2} to get -243x^{2}.

$$-243x^{2}-42x+49-108x^{3}+588x+1372$$

Combine -42x and 588x to get 546x.

$$-243x^{2}+546x+49-108x^{3}+1372$$

Add 49 and 1372 to get 1421.

$$-243x^{2}+546x+1421-108x^{3}$$