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
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
_______________________
Thanks for the question !
BrainlyQueen01:
Thanks dear :)
Answered by
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
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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