Solve y=(x+5)(x+2)^2(x-4)/25

$$y = \frac { ( x + 5 ) ( x + 2 ) ^ { 2 } ( x - 4 ) } { 25 }$$

Solve for y

$$y=\frac{\left(x-4\right)\left(x+5\right)\left(x+2\right)^{2}}{25}$$

Solution Steps

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

$$y=\frac{\left(x+5\right)\left(x^{2}+4x+4\right)\left(x-4\right)}{25}$$

Use the distributive property to multiply x+5 by x^{2}+4x+4 and combine like terms.

$$y=\frac{\left(x^{3}+9x^{2}+24x+20\right)\left(x-4\right)}{25}$$

Use the distributive property to multiply x^{3}+9x^{2}+24x+20 by x-4 and combine like terms.

$$y=\frac{x^{4}+5x^{3}-12x^{2}-76x-80}{25}$$

Divide each term of x^{4}+5x^{3}-12x^{2}-76x-80 by 25 to get \frac{1}{25}x^{4}+\frac{1}{5}x^{3}-\frac{12}{25}x^{2}-\frac{76}{25}x-\frac{16}{5}.

$$y=\frac{1}{25}x^{4}+\frac{1}{5}x^{3}-\frac{12}{25}x^{2}-\frac{76}{25}x-\frac{16}{5}$$