What is expand (x+2)(x+3)(x+4)(x+5) ?

The solution to expand (x+2)(x+3)(x+4)(x+5) is x^4+14x^3+71x^2+154x+120

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expand (x+2)(x+3)(x+4)(x+5)

expand

(x + 2) (x + 3) (x + 4) (x + 5)

x^{4} + 14 x^{3} + 71 x^{2} + 154 x + 120

Solution steps

(x + 2) (x + 3) (x + 4) (x + 5)

Expand

(x + 2) (x + 3) (x + 4) (x + 5) : (x^{2} + 5 x + 6) (x + 4) (x + 5)

= (x^{2} + 5 x + 6) (x + 4) (x + 5)

Apply FOIL method

(x + 4) (x + 5) : x^{2} + 9 x + 20

= (x^{2} + 5 x + 6) (x^{2} + 9 x + 20)

Distribute parentheses

= x^{2} x^{2} + x^{2} \cdot 9 x + x^{2} \cdot 20 + 5 x x^{2} + 5 x \cdot 9 x + 5 x \cdot 20 + 6 x^{2} + 6 \cdot 9 x + 6 \cdot 20

Simplify

x^{2} x^{2} + x^{2} \cdot 9 x + x^{2} \cdot 20 + 5 x x^{2} + 5 x \cdot 9 x + 5 x \cdot 20 + 6 x^{2} + 6 \cdot 9 x + 6 \cdot 20 : x^{4} + 14 x^{3} + 71 x^{2} + 154 x + 120

= x^{4} + 14 x^{3} + 71 x^{2} + 154 x + 120

- 8 i^{2} + 3

\frac{m ^{2} n}{m ^{5} n ^{3}}

(3 x - 5) (2 x + 7)

\frac{20 !}{5 ! ( 20 - 5 ) !}

43 + 4 i

What is expand (x+2)(x+3)(x+4)(x+5) ?
The solution to expand (x+2)(x+3)(x+4)(x+5) is x^4+14x^3+71x^2+154x+120