Question

Factorize: X²+20X + 100​

Answer 1

Use the sum-product pattern

2+20+100

x^{2}+{\color{#c92786}{20x}}+100x2+20x+100

2+10+10+100

x^{2}+{\color{#c92786}{10x}}+{\color{#c92786}{10x}}+100x2+10x+10x+100

2

Common factor from the two pairs

2+10+10+100

x^{2}+10x+10x+100x2+10x+10x+100

(+10)+10(+10)

x(x+10)+10(x+10)x(x+10)+10(x+10)

3

Rewrite in factored form

(+10)+10(+10)

x(x+10)+10(x+10)x(x+10)+10(x+10)

(+10)(+10)

(x+10)(x+10)(x+10)(x+10)

4

Combine to a square

(+10)(+10)

(x+10)(x+10)(x+10)(x+10)

(+10)2