which of the following is equivalent to (x+5)^2

Question

Which of the following is equivalent to (x+5)^2

(A) x^2+10x+25

(B) x^2+25

(C) 2x+25

(D) 2x+10

Answer 1

(x+5)^2 can be written (x+5)*(x+5).

 

You can then use FOIL to find the answer. Don't forget to add the two middle terms (both equal to something times x).

Answer 2

(x + 5) squared means (x + 5) times (x + 5), so we square the first terms of each binomial (x^2), then multiply 2nd term of 1st binomial times 1st term of second binomial (5x), then multiply 1st term of 2nd binomial times 1st term of 1st binomial (5x), then 2nd terms of each binomial (25), then add these 4 products together and combine terms. This gives us: x^2 + 5x + 5x + 25 = x^2 + 10x + 25, so correct answer is A. 

Answer 3

(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25

 

(A) is correct.

 

Are you familiar with Paschal's triangle to get the coefficients?

 

1 

1 2 1

1 3 3 1

etc.

Answer 4

(x+5)^2

= (x+5)(x+5)

= x^2 +5x + 5x + 25

= x^2 + 10x + 25