Solve 3(2x+5)^2-4(2x+5)(2x-5)+10(2x-5)^2=

$$3 ( 2 x + 5 ) ^ { 2 } - 4 ( 2 x + 5 ) ( 2 x - 5 ) + 10 ( 2 x - 5 ) ^ { 2 } =$$

Evaluate

$$36x^{2}-140x+425$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5\right)^{2}.

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Use the distributive property to multiply 3 by 4x^{2}+20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

Use the distributive property to multiply 10 by 4x^{2}-20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

Use the distributive property to multiply -4 by 2x+5.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

Use the distributive property to multiply -8x-20 by 2x-5 and combine like terms.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

Combine 12x^{2} and -16x^{2} to get -4x^{2}.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

Add 75 and 100 to get 175.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

Combine -4x^{2} and 40x^{2} to get 36x^{2}.

$$36x^{2}+60x+175-200x+250$$

Combine 60x and -200x to get -140x.

$$36x^{2}-140x+175+250$$

Add 175 and 250 to get 425.

$$36x^{2}-140x+425$$

Expand

$$36x^{2}-140x+425$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5\right)^{2}.

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Use the distributive property to multiply 3 by 4x^{2}+20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

Use the distributive property to multiply 10 by 4x^{2}-20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

Use the distributive property to multiply -4 by 2x+5.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

Use the distributive property to multiply -8x-20 by 2x-5 and combine like terms.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

Combine 12x^{2} and -16x^{2} to get -4x^{2}.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

Add 75 and 100 to get 175.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

Combine -4x^{2} and 40x^{2} to get 36x^{2}.

$$36x^{2}+60x+175-200x+250$$

Combine 60x and -200x to get -140x.

$$36x^{2}-140x+175+250$$

Add 175 and 250 to get 425.

$$36x^{2}-140x+425$$