Solve (a-3b)^2-2a(b-a)+b(3a+b)

$$( a - 3 b ) ^ { 2 } - 2 a ( b - a ) + b ( 3 a + b )$$

Evaluate

$$3a^{2}-5ab+10b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.

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

Use the distributive property to multiply b by 3a+b.

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

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

$$a^{2}-6ab+9b^{2}-2ab+2a^{2}+3ba+b^{2}$$

Combine -6ab and -2ab to get -8ab.

$$a^{2}-8ab+9b^{2}+2a^{2}+3ba+b^{2}$$

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

$$3a^{2}-8ab+9b^{2}+3ba+b^{2}$$

Combine -8ab and 3ba to get -5ab.

$$3a^{2}-5ab+9b^{2}+b^{2}$$

Combine 9b^{2} and b^{2} to get 10b^{2}.

$$3a^{2}-5ab+10b^{2}$$

Expand

$$3a^{2}-5ab+10b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-3b\right)^{2}.

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

Use the distributive property to multiply b by 3a+b.

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

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

$$a^{2}-6ab+9b^{2}-2ab+2a^{2}+3ba+b^{2}$$

Combine -6ab and -2ab to get -8ab.

$$a^{2}-8ab+9b^{2}+2a^{2}+3ba+b^{2}$$

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

$$3a^{2}-8ab+9b^{2}+3ba+b^{2}$$

Combine -8ab and 3ba to get -5ab.

$$3a^{2}-5ab+9b^{2}+b^{2}$$

Combine 9b^{2} and b^{2} to get 10b^{2}.

$$3a^{2}-5ab+10b^{2}$$