Question

Factor the expression. c2 + 10c + 25 A. (c + 5)2 B. (c – 5)2 C. (c + 5)(c – 5)

Answer 1

(c + 5)2

Explanation:

c2 + 10c + 25

= c • c + 10c + 5 • 5

= c • c + 2(c • 5) + 5 • 5

= (c + 5)2

Answer 2

`\large\boxed{c^2+10c+25=(c+5)^2}`

Explanation:

`METHOD\ 1:\\\\c^2+10c+25=c^2+5c+5c+25=c(c+5)+5(c+5)=(c+5)(c+5)\\\\\boxed{c^2+10c+25=(c+5)^2}\\\\METHOD\ 2:\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\c^2+10c+25=c^2+2(c)(5)+5^2\\\\\boxed{c^2+10c+25=(c+5)^2}`