Question

x^2 - a^2 = (x+a)(x-a)

Use the polynomial identity above to rewrite x^2 −196

x^2−196=(x−14)(x−14)

x^2 −196=(x−98)(x−98)

x^2 −196=(x+14)(x−14)

x^2 −196=(x+98)(x−98)

Answer 1

Since 196 = 14^2, take a = 14. Then by x^2 − a^2 = (x + a)(x − a),

x^2 − 196 = x^2 − 14^2 = (x + 14)(x − 14).

(The other listed factorizations are incorrect — e.g. (x − 14)^2 expands to x^2 − 28x + 196, not x^2 − 196.)