Solve (4x-a)(4x+a)+2x(x-a)

$$( 4 x - a ) ( 4 x + a ) + 2 x ( x - a )$$

Evaluate

$$18x^{2}-2ax-a^{2}$$

Solution Steps

Consider \left(4x-a\right)\left(4x+a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(4x\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-a^{2}+2x\left(x-a\right)$$

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

$$16x^{2}-a^{2}+2x^{2}-2xa$$

Combine 16x^{2} and 2x^{2} to get 18x^{2}.

$$18x^{2}-a^{2}-2xa$$

Expand

$$18x^{2}-2ax-a^{2}$$

Solution Steps

Consider \left(4x-a\right)\left(4x+a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(4x\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16x^{2}-a^{2}+2x\left(x-a\right)$$

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

$$16x^{2}-a^{2}+2x^{2}-2xa$$

Combine 16x^{2} and 2x^{2} to get 18x^{2}.

$$18x^{2}-a^{2}-2xa$$