Solve left(5x+2right)^2+left(2x-1right)left(2x+1right)-3left(x-2right)

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

Evaluate

$$29x^{2}+17x+9$$

Solution Steps

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

$$25x^{2}+20x+4+\left(2x-1\right)\left(2x+1\right)-3\left(x-2\right)$$

Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$25x^{2}+20x+4+\left(2x\right)^{2}-1-3\left(x-2\right)$$

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

$$25x^{2}+20x+4+2^{2}x^{2}-1-3\left(x-2\right)$$

Calculate 2 to the power of 2 and get 4.

$$25x^{2}+20x+4+4x^{2}-1-3\left(x-2\right)$$

Combine 25x^{2} and 4x^{2} to get 29x^{2}.

$$29x^{2}+20x+4-1-3\left(x-2\right)$$

Subtract 1 from 4 to get 3.

$$29x^{2}+20x+3-3\left(x-2\right)$$

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

$$29x^{2}+20x+3-3x+6$$

Combine 20x and -3x to get 17x.

$$29x^{2}+17x+3+6$$

Add 3 and 6 to get 9.

$$29x^{2}+17x+9$$

Expand

$$29x^{2}+17x+9$$

Solution Steps

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

$$25x^{2}+20x+4+\left(2x-1\right)\left(2x+1\right)-3\left(x-2\right)$$

Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$25x^{2}+20x+4+\left(2x\right)^{2}-1-3\left(x-2\right)$$

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

$$25x^{2}+20x+4+2^{2}x^{2}-1-3\left(x-2\right)$$

Calculate 2 to the power of 2 and get 4.

$$25x^{2}+20x+4+4x^{2}-1-3\left(x-2\right)$$

Combine 25x^{2} and 4x^{2} to get 29x^{2}.

$$29x^{2}+20x+4-1-3\left(x-2\right)$$

Subtract 1 from 4 to get 3.

$$29x^{2}+20x+3-3\left(x-2\right)$$

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

$$29x^{2}+20x+3-3x+6$$

Combine 20x and -3x to get 17x.

$$29x^{2}+17x+3+6$$

Add 3 and 6 to get 9.

$$29x^{2}+17x+9$$