Solve 3a(a-2)-(5a-1)(a+1)

$$3 a ( a - 2 ) - ( 5 a - 1 ) ( a + 1 )$$

Evaluate

$$1-10a-2a^{2}$$

Solution Steps

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

$$3a^{2}-6a-\left(5a-1\right)\left(a+1\right)$$

Apply the distributive property by multiplying each term of 5a-1 by each term of a+1.

$$3a^{2}-6a-\left(5a^{2}+5a-a-1\right)$$

Combine 5a and -a to get 4a.

$$3a^{2}-6a-\left(5a^{2}+4a-1\right)$$

To find the opposite of 5a^{2}+4a-1, find the opposite of each term.

$$3a^{2}-6a-5a^{2}-4a-\left(-1\right)$$

The opposite of -1 is 1.

$$3a^{2}-6a-5a^{2}-4a+1$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$-2a^{2}-6a-4a+1$$

Combine -6a and -4a to get -10a.

$$-2a^{2}-10a+1$$

Expand

$$1-10a-2a^{2}$$

Solution Steps

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

$$3a^{2}-6a-\left(5a-1\right)\left(a+1\right)$$

Apply the distributive property by multiplying each term of 5a-1 by each term of a+1.

$$3a^{2}-6a-\left(5a^{2}+5a-a-1\right)$$

Combine 5a and -a to get 4a.

$$3a^{2}-6a-\left(5a^{2}+4a-1\right)$$

To find the opposite of 5a^{2}+4a-1, find the opposite of each term.

$$3a^{2}-6a-5a^{2}-4a-\left(-1\right)$$

The opposite of -1 is 1.

$$3a^{2}-6a-5a^{2}-4a+1$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$-2a^{2}-6a-4a+1$$

Combine -6a and -4a to get -10a.

$$-2a^{2}-10a+1$$