Math, asked by adarsh70000, 1 year ago

10.Factorize the following:
a)x^2-8x+16.
b)9x^2-12x+4.
c)4y^2-12y+9.
d)p^2y^2-2py+1.

Answers

Answered by BrainlyQueen01
65

Answer :


a) ( x - 4 )²


b) ( 3x - 2 )²


c) ( 2y - 3 )²


d) ( py - 1 )²


Step-by-step explanation :


a) x² - 8 x + 16


On splitting the middle term ;


⇒ x² - 4x - 4x + 16


⇒ x ( x - 4 ) - 4 ( x - 4 )


⇒ ( x - 4 ) ( x - 4 )


⇒ ( x - 4 )²


_______________________


b) 9x² - 12 x + 4


On splitting the middle term ;


⇒ 9x² - 6x - 6x + 4


⇒ 3x ( 3x - 2 ) - 2 ( 3x - 2 )


⇒ ( 3x - 2 ) ( 3x - 2 )


⇒ ( 3x - 2 )²


_______________________


c) 4y² - 12y + 9


On splitting the middle term ;


⇒ 4y² - 6y - 6y + 9


⇒ 2y ( 2y - 3 ) - ( 2y - 3 )


⇒ ( 2y - 3 ) ( 2y - 3 )


⇒ ( 2y - 3 )²


_______________________


d) p²y² - 2py + 1


On splitting the middle term ;


⇒ p²y² - 1 py - 1 py +1


⇒ py ( py - 1 ) - 1 ( py - 1 )


⇒ ( py - 1 ) ( py - 1 )


( py - 1 )²


_______________________


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Answered by kshitij2211
35
→a) x²-8x+16
x²-4x-4x+16
x(x-4)-4(x-4)
(x-4)(x-4)
or
(x-4)²

→b) 9x²-12x+4
9x²-6x-6x+4
3x(3x-2)-2(3x-2)
(3x-2)(3x-2)
or
(3x-2)²

→c) 4y²-12y+9
4y²-6y-6y+9
2y(2y-3)-3(2y-3)
(2y-3)(2y-3)
or
(2y-3)²

→d) p²y²-2py+1
p²y²-py-py+1
py(py-1)-1(py-1)
(py-1)(py-1)
or
(py-1)²
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