Solve (x+2)(x*7)(x+3)^3

$$( x + 2 ) ( x \times 7 ) ( x + 3 ) ^ { 3 }$$

Evaluate

$$7x\left(x+2\right)\left(x+3\right)^{3}$$

Solution Steps

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

$$\left(x+2\right)x\times 7\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply x+2 by x.

$$\left(x^{2}+2x\right)\times 7\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply x^{2}+2x by 7.

$$\left(7x^{2}+14x\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 7x^{2}+14x by x^{3}+9x^{2}+27x+27 and combine like terms.

$$7x^{5}+77x^{4}+315x^{3}+567x^{2}+378x$$

Expand

$$7x^{5}+77x^{4}+315x^{3}+567x^{2}+378x$$

Solution Steps

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

$$\left(x+2\right)x\times 7\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply x+2 by x.

$$\left(x^{2}+2x\right)\times 7\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply x^{2}+2x by 7.

$$\left(7x^{2}+14x\right)\left(x^{3}+9x^{2}+27x+27\right)$$

Use the distributive property to multiply 7x^{2}+14x by x^{3}+9x^{2}+27x+27 and combine like terms.

$$7x^{5}+77x^{4}+315x^{3}+567x^{2}+378x$$