Solve left(x+5right)^2-5(2x+1)(2x-1)+x*left(2xright)^2

$${ \left(x+5 \right) }^{ 2 } -5(2x+1)(2x-1)+x \times { \left(2x \right) }^{ 2 }$$

Evaluate

$$4x^{3}-19x^{2}+10x+30$$

Solution Steps

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

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times \left(2x\right)^{2}$$

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

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times 2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times 4x^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x^{3}\times 4$$

Use the distributive property to multiply -5 by 2x+1.

$$x^{2}+10x+25+\left(-10x-5\right)\left(2x-1\right)+x^{3}\times 4$$

Use the distributive property to multiply -10x-5 by 2x-1 and combine like terms.

$$x^{2}+10x+25-20x^{2}+5+x^{3}\times 4$$

Combine x^{2} and -20x^{2} to get -19x^{2}.

$$-19x^{2}+10x+25+5+x^{3}\times 4$$

Add 25 and 5 to get 30.

$$-19x^{2}+10x+30+x^{3}\times 4$$

Expand

$$4x^{3}-19x^{2}+10x+30$$

Solution Steps

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

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times \left(2x\right)^{2}$$

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

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times 2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x\times 4x^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{2}+10x+25-5\left(2x+1\right)\left(2x-1\right)+x^{3}\times 4$$

Use the distributive property to multiply -5 by 2x+1.

$$x^{2}+10x+25+\left(-10x-5\right)\left(2x-1\right)+x^{3}\times 4$$

Use the distributive property to multiply -10x-5 by 2x-1 and combine like terms.

$$x^{2}+10x+25-20x^{2}+5+x^{3}\times 4$$

Combine x^{2} and -20x^{2} to get -19x^{2}.

$$-19x^{2}+10x+25+5+x^{3}\times 4$$

Add 25 and 5 to get 30.

$$-19x^{2}+10x+30+x^{3}\times 4$$