Solve 5x(x-3)*(2x-1)(x-3)

$$5 x ( x - 3 ) \cdot ( 2 x - 1 ) ( x - 3 )$$

Evaluate

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

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

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

$$5x\left(x^{2}-6x+9\right)\left(2x-1\right)$$

Use the distributive property to multiply 5x by x^{2}-6x+9.

$$\left(5x^{3}-30x^{2}+45x\right)\left(2x-1\right)$$

Apply the distributive property by multiplying each term of 5x^{3}-30x^{2}+45x by each term of 2x-1.

$$10x^{4}-5x^{3}-60x^{3}+30x^{2}+90x^{2}-45x$$

Combine -5x^{3} and -60x^{3} to get -65x^{3}.

$$10x^{4}-65x^{3}+30x^{2}+90x^{2}-45x$$

Combine 30x^{2} and 90x^{2} to get 120x^{2}.

$$10x^{4}-65x^{3}+120x^{2}-45x$$

Expand

$$10x^{4}-65x^{3}+120x^{2}-45x$$

Solution Steps

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

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

$$5x\left(x^{2}-6x+9\right)\left(2x-1\right)$$

Use the distributive property to multiply 5x by x^{2}-6x+9.

$$\left(5x^{3}-30x^{2}+45x\right)\left(2x-1\right)$$

Apply the distributive property by multiplying each term of 5x^{3}-30x^{2}+45x by each term of 2x-1.

$$10x^{4}-5x^{3}-60x^{3}+30x^{2}+90x^{2}-45x$$

Combine -5x^{3} and -60x^{3} to get -65x^{3}.

$$10x^{4}-65x^{3}+30x^{2}+90x^{2}-45x$$

Combine 30x^{2} and 90x^{2} to get 120x^{2}.

$$10x^{4}-65x^{3}+120x^{2}-45x$$