Factor the expression by grouping. First, the expression needs to be rewritten as y^2+ay+by+9. To find a and b, set up a system to be solved.
a+b=−6
ab=1×9=9
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 9.
−1,−9
−3,−3
Calculate the sum for each pair.
−1−9=−10
−3−3=−6
The solution is the pair that gives sum −6.
a=−3
b=−3
Rewrite y^2 −6y+9 as (y^2−3y)+(−3y+9).
(y^2 −3y)+(−3y+9)
Factor out y in the first and −3 in the second group.
y(y−3)−3(y−3)
Factor out common term y−3 by using the distributive property.
(y−3)(y−3)
Rewrite as a binomial square.
Answer: (y−3)^2
2.) 4x^2-4x+1= (2x-1)^2
4x^2−4x+1
Factor the expression by grouping. First, the expression needs to be rewritten as 4x^2+ax+bx+1. To find a and b, set up a system to be solved.
a+b=−4
ab=4×1=4
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 4.
−1,−4
−2,−2
Calculate the sum for each pair.
−1−4=−5
−2−2=−4
The solution is the pair that gives sum −4.
a=−2
b=−2
Rewrite 4x^ 2−4x+1 as (4x^2−2x)+(−2x+1).
(4x^2−2x)+(−2x+1)
Factor out 2x in the first and −1 in the second group.
2x(2x−1)−(2x−1)
Factor out common term 2x−1 by using the distributive property.
(2x−1)(2x−1)
Rewrite as a binomial square.
Answer: (2x−1)^2
#CarryOnLearning
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Answers & Comments
Question:
1.) y^2+6y+9
2.) 4x^2-4x+1
Answer:
1.) y^2+6y+9 = (y−3)^2
y^2 −6y+9
Factor the expression by grouping. First, the expression needs to be rewritten as y^2+ay+by+9. To find a and b, set up a system to be solved.
a+b=−6
ab=1×9=9
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 9.
−1,−9
−3,−3
Calculate the sum for each pair.
−1−9=−10
−3−3=−6
The solution is the pair that gives sum −6.
a=−3
b=−3
Rewrite y^2 −6y+9 as (y^2−3y)+(−3y+9).
(y^2 −3y)+(−3y+9)
Factor out y in the first and −3 in the second group.
y(y−3)−3(y−3)
Factor out common term y−3 by using the distributive property.
(y−3)(y−3)
Rewrite as a binomial square.
Answer: (y−3)^2
2.) 4x^2-4x+1= (2x-1)^2
4x^2−4x+1
Factor the expression by grouping. First, the expression needs to be rewritten as 4x^2+ax+bx+1. To find a and b, set up a system to be solved.
a+b=−4
ab=4×1=4
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 4.
−1,−4
−2,−2
Calculate the sum for each pair.
−1−4=−5
−2−2=−4
The solution is the pair that gives sum −4.
a=−2
b=−2
Rewrite 4x^ 2−4x+1 as (4x^2−2x)+(−2x+1).
(4x^2−2x)+(−2x+1)
Factor out 2x in the first and −1 in the second group.
2x(2x−1)−(2x−1)
Factor out common term 2x−1 by using the distributive property.
(2x−1)(2x−1)
Rewrite as a binomial square.
Answer: (2x−1)^2
#CarryOnLearning
Hello brainly users please use this hashtag #CarryOnLearning to support our friends and our heroes in the medical field. if you use this hashtag in your answer is equivalent for a peso donation for our heroes that tired in the hospitals. Stay home, stay safe,