Question

factorize: ( x+ 998) (x +999) -1000/(999)²​

Answer 1

Step-by-step explanation:

Distribute

(+998)(+999)−1⋅1000(999)2

{\color{#c92786}{(x+998)(x+999)}}-1 \cdot \frac{1000}{(999)^{2}}(x+998)(x+999)−1⋅(999)21000

(+999)+998(+999)−1⋅1000(999)2

{\color{#c92786}{x(x+999)+998(x+999)}}-1 \cdot \frac{1000}{(999)^{2}}x(x+999)+998(x+999)−1⋅(999)21000

2

Distribute

(+999)+998(+999)−1⋅1000(999)2

{\color{#c92786}{x(x+999)}}+998(x+999)-1 \cdot \frac{1000}{(999)^{2}}x(x+999)+998(x+999)−1⋅(999)21000

2+999+998(+999)−1⋅1000(999)2

{\color{#c92786}{x^{2}+999x}}+998(x+999)-1 \cdot \frac{1000}{(999)^{2}}x2+999x+998(x+999)−1⋅(999)21000

3

Distribute

2+999+998(+999)−1⋅1000(999)2

x^{2}+999x+{\color{#c92786}{998(x+999)}}-1 \cdot \frac{1000}{(999)^{2}}x2+999x+998(x+999)−1⋅(999)21000

2+999+998+997002−1⋅1000(999)2

x^{2}+999x+{\color{#c92786}{998x+997002}}-1 \cdot \frac{1000}{(999)^{2}}x2+999x+998x+997002−1⋅(999)21000

4

Combine like terms

2+999+998+997002−1⋅1000(999)2

x^{2}+{\color{#c92786}{999x}}+{\color{#c92786}{998x}}+997002-1 \cdot \frac{1000}{(999)^{2}}x2+999x+998x+997002−1⋅(999)21000

2+1997+997002−1⋅1000(999)2

x^{2}+{\color{#c92786}{1997x}}+997002-1 \cdot \frac{1000}{(999)^{2}}x2+1997x+997002−1⋅(999)21000

5

Evaluate the exponent

2+1997+997002−1⋅10009992

x^{2}+1997x+997002-1 \cdot \frac{1000}{{\color{#c92786}{999^{2}}}}x2+1997x+997002−1⋅99921000

2+1997+997002−1⋅1000998001

x^{2}+1997x+997002-1 \cdot \frac{1000}{{\color{#c92786}{998001}}}x2+1997x+997002−1⋅9980011000

6

Multiply the numbers

2+1997+997002−1⋅1000998001

x^{2}+1997x+997002{\color{#c92786}{-1}} \cdot {\color{#c92786}{\frac{1000}{998001}}}x2+1997x+997002−1⋅9980011000

2+1997+997002−1000998001

x^{2}+1997x+997002{\color{#c92786}{-\frac{1000}{998001}}}x2+1997x+997002−9980011000