Solve 36left(2a+bright)left(4b-5aright)-left(a-3bright)left(2b-3aright)

$$36 \left( 2a+b \right) \left( 4b-5a \right) - \left( a-3b \right) \left( 2b-3a \right)$$

Evaluate

$$150b^{2}+97ab-357a^{2}$$

Solution Steps

Use the distributive property to multiply 36 by 2a+b.

$$\left(72a+36b\right)\left(4b-5a\right)-\left(a-3b\right)\left(2b-3a\right)$$

Apply the distributive property by multiplying each term of 72a+36b by each term of 4b-5a.

$$288ab-360a^{2}+144b^{2}-180ba-\left(a-3b\right)\left(2b-3a\right)$$

Combine 288ab and -180ba to get 108ab.

$$108ab-360a^{2}+144b^{2}-\left(a-3b\right)\left(2b-3a\right)$$

Apply the distributive property by multiplying each term of a-3b by each term of 2b-3a.

$$108ab-360a^{2}+144b^{2}-\left(2ab-3a^{2}-6b^{2}+9ba\right)$$

Combine 2ab and 9ba to get 11ab.

$$108ab-360a^{2}+144b^{2}-\left(11ab-3a^{2}-6b^{2}\right)$$

To find the opposite of 11ab-3a^{2}-6b^{2}, find the opposite of each term.

$$108ab-360a^{2}+144b^{2}-11ab-\left(-3a^{2}\right)-\left(-6b^{2}\right)$$

The opposite of -3a^{2} is 3a^{2}.

$$108ab-360a^{2}+144b^{2}-11ab+3a^{2}-\left(-6b^{2}\right)$$

The opposite of -6b^{2} is 6b^{2}.

$$108ab-360a^{2}+144b^{2}-11ab+3a^{2}+6b^{2}$$

Combine 108ab and -11ab to get 97ab.

$$97ab-360a^{2}+144b^{2}+3a^{2}+6b^{2}$$

Combine -360a^{2} and 3a^{2} to get -357a^{2}.

$$97ab-357a^{2}+144b^{2}+6b^{2}$$

Combine 144b^{2} and 6b^{2} to get 150b^{2}.

$$97ab-357a^{2}+150b^{2}$$

Expand

$$150b^{2}+97ab-357a^{2}$$

Solution Steps

Use the distributive property to multiply 36 by 2a+b.

$$\left(72a+36b\right)\left(4b-5a\right)-\left(a-3b\right)\left(2b-3a\right)$$

Apply the distributive property by multiplying each term of 72a+36b by each term of 4b-5a.

$$288ab-360a^{2}+144b^{2}-180ba-\left(a-3b\right)\left(2b-3a\right)$$

Combine 288ab and -180ba to get 108ab.

$$108ab-360a^{2}+144b^{2}-\left(a-3b\right)\left(2b-3a\right)$$

Apply the distributive property by multiplying each term of a-3b by each term of 2b-3a.

$$108ab-360a^{2}+144b^{2}-\left(2ab-3a^{2}-6b^{2}+9ba\right)$$

Combine 2ab and 9ba to get 11ab.

$$108ab-360a^{2}+144b^{2}-\left(11ab-3a^{2}-6b^{2}\right)$$

To find the opposite of 11ab-3a^{2}-6b^{2}, find the opposite of each term.

$$108ab-360a^{2}+144b^{2}-11ab-\left(-3a^{2}\right)-\left(-6b^{2}\right)$$

The opposite of -3a^{2} is 3a^{2}.

$$108ab-360a^{2}+144b^{2}-11ab+3a^{2}-\left(-6b^{2}\right)$$

The opposite of -6b^{2} is 6b^{2}.

$$108ab-360a^{2}+144b^{2}-11ab+3a^{2}+6b^{2}$$

Combine 108ab and -11ab to get 97ab.

$$97ab-360a^{2}+144b^{2}+3a^{2}+6b^{2}$$

Combine -360a^{2} and 3a^{2} to get -357a^{2}.

$$97ab-357a^{2}+144b^{2}+6b^{2}$$

Combine 144b^{2} and 6b^{2} to get 150b^{2}.

$$97ab-357a^{2}+150b^{2}$$