Factorise the following.
(i) 7 a2 + 7 a – 42
(ii) y2 + 19 y – 150
(iii) 3 x2 + 48 x +117
Answers
Step-by-step explanation:
Given :-
(i) 7 a^2 + 7 a – 42
(ii) y^2 + 19 y – 150
(iii) 3 x^2 + 48 x +117
To find:-
Factorise the given expresiona ?
Solution :-
Given expressions :
(i) 7 a^2 + 7 a – 42
=> 7 ( a^2 + a - 6 )
=> 7 ( a^2 + 3a - 2a - 6 )
=>7 ( a ( a + 3 ) - 2 ( a + 3 ) )
=> 7 ( a + 3 ) ( a - 2 )
7 a^2 + 7 a – 42 = 7 ( a + 3 ) ( a - 2 )
_______________________________
(ii) y^2 + 19 y – 150
=> y^2 -6y +25 y - 150
=> y ( y - 6 ) + 25 ( y - 6 )
=> ( y - 6 ) ( y + 25 )
y^2 + 19 y – 150 = ( y - 6 ) ( y + 25 )
_______________________________
(iii)3 x^2 + 48 x +117
=> 3 ( x^2 + 16x + 39 )
=> 3 ( x^2 + 3x + 13x + 39 )
=> 3 ( x ( x + 3 ) + 13 ( x + 13 ) )
=>3 ( x + 3 ) ( x + 13 )
3 x^2 + 48 x +117 = 3 ( x + 3 ) ( x + 13 )
_______________________________
Answer:-
(I)7 a^2 + 7 a – 42 = 7 ( a + 3 ) ( a - 2 )
(ii)y^2 + 19 y – 150 = ( y - 6 ) ( y + 25 )
(iii) 3 x^2 + 48 x +117 = 3 ( x + 3 ) ( x + 13 )
Used Method :-
- Splitting the middle term