Write each of the following as a trinomial of the form ax^2 + bx + c
A.
(x + 2)^2
B.
(x - 5)^2
C.
(x + 4)^2
recall that (a+b)^2 = a^2 + 2ab + b^2
so, the second one is
(x - 5)^2 = x^2 - 10x + 25
do the others in like wise. Consult your text for other examples, or use google if needed.
To write each of the expressions as a trinomial of the form ax^2 + bx + c, we need to expand the squared expression.
A. (x + 2)^2
To expand the squared expression (x + 2)^2, we can use the formula (a + b)^2 = a^2 + 2ab + b^2.
Here, a = x, and b = 2. So we have:
(x + 2)^2 = x^2 + 2(x)(2) + 2^2
= x^2 + 4x + 4
Therefore, A can be written as the trinomial x^2 + 4x + 4.
B. (x - 5)^2
To expand the squared expression (x - 5)^2, we can again use the formula (a - b)^2 = a^2 - 2ab + b^2.
Here, a = x, and b = 5. So we have:
(x - 5)^2 = x^2 - 2(x)(5) + 5^2
= x^2 - 10x + 25
Therefore, B can be written as the trinomial x^2 - 10x + 25.
C. (x + 4)^2
To expand the squared expression (x + 4)^2, we can once more use the formula (a + b)^2 = a^2 + 2ab + b^2.
Here, a = x, and b = 4. So we have:
(x + 4)^2 = x^2 + 2(x)(4) + 4^2
= x^2 + 8x + 16
Therefore, C can be written as the trinomial x^2 + 8x + 16.
So, the trinomials of the given expressions are:
A. x^2 + 4x + 4
B. x^2 - 10x + 25
C. x^2 + 8x + 16