Activity 3: Square Me!Express each of the following perfect square trinomials as...

Questions

October 2022 1 1 Report

Activity 3: Square Me!
Express each of the following perfect square trinomials as a square of a binomial.

1. x² + 2x + 1 = (______)²
2. x² − 4x + 4 = (_____)²
3. n² + 6n + 9 = (_____)²
4. h² − 22h + 121 = (_____)²
5. r² − 7r + 49 4 = (_____)²

Answers & Comments

Prodigy43

$\Huge\mathbb{ANSWER}$

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$x²−2x+1 \\ =x²−2x+12 \\ =(x−1)²$

A perfect square trinomial is the square of a binomial, so will take the form:

a²+2ab+b²

since

(a+b)2=a2+2ab+b2

So a perfect square trinomial satisfies the following conditions:

(1) Two of the terms are squares.

(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.

If the two square terms are a2 and b2 then the trinomial is either (a+b)2 or (a−b)2 depending on the sign of the third term

$\large \therefore \underline{\boxed{\tt \green{(x−1)²}}}$

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$\tiny\mathfrak{CarryOnLearning}$

Prodigy43 x2−2⋅x⋅2+22

Prodigy43 a²−2ab+b²=(a−b)²

Prodigy43 answer for no. 2 = (x−2)²

shi0143 ty po, btw the no. 3, 4, 5 po?

Prodigy43 3. n² + 6n + 9 = (_____)²
Rewrite 9 as 3²
n²+6n+3²
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
6n=2⋅n⋅3
Rewrite the polynomial.
n²+2⋅n⋅3+3²
Factor using the perfect square trinomial rule
a²+2ab+b²=(a+b)²
where a=n & b=3
Answer: (n+3)2

Prodigy43 (n+3)²*

Prodigy43 sorry nakalimutan kotoh ituloy kahapon

Prodigy43 4. h² − 22h + 121 = (_____)²
(1): "h2"   was replaced by   "h^2"
h²-22h+121
   1 • 121 = 121
     -121   +   -1   =   -122     -11   +   -11   =   -22
                     h2 - 11h - 11h - 121
                    h • (h-11)
                    11 • (h-11)
(h-11)  •  (h-11)
             Multiply (h-11) by (h-11)
          1 , as  (h-11) is the same number as (h-11)1
and   1 , as  (h-11) is the same number as (h-11)1
(h-11)(1+1)
Answer = (h-11)²

Prodigy43 5. r² − 7r + 49/4 = (_____)²
a=1,b=−7,c=49/4
a(x+d)²+e
d=−7/2(1)
d=−7/2
e=49/4−49/4(1)
e=49/4−49/4
e=49−49/4
e=0/4
e=0
Substitute the values of a,d & e into the vertex form
= (x+d)2+e
= a(x+d)2+e
Answer: = (r-7/2)²+0 or (r-7/2)²