Resolve into factors (any two):
(a) (a² -4ab) - (c2-4bc)
(b) (1 + x) (y - Z) + (1 + z) (x - y)
(c) a4 + a2x2 + x4
+
Answers
Answer:
Step-by-step explanation:
Factorisationa
3
+ b
3
+ c
3
– 3abc = (a + b + c)(a
2
+ b
2
+ c
2
– ab – bc – ca)a
3
+ b
3
+ c
3
– 3abc = ½{(a + b)
3
+ (b + c)
3
+ (c + a)
3
– 3(a + b)(b + c)(c +a)}a
3
+ b
3
+ c
3
– 3abc = ½(a + b + c){(a – b)
2
+ (b – c)
2
+ (c – a)
2
}a
3
+ b
3
+ c
3
= (a + b + c)
3
– 3(a + b)(b + c)(c + a)Level – 1
1.
Factorise x
4
– 14x
2
y
2
+ y
4
x
4
– 14x
2
y
2
+ y
4
= x
4
+ 2x
2
y
2
+ y
4
– 16x
2
y
2
= (x
2
+ y
2
)
2
– (4xy)
2
= (x
2
+ y
2
+ 4xy) (x
2
+ y
2
– 4xy)
2.
Factorise (x
2
+ x + 1)(x
2
+ x + 2) – 12Let x
2
+ x + 1 = a(x
2
+ x + 1)(x
2
+ x + 2) – 12= a(a + 1) – 12= a
2
+ a – 12= (a + 4)(a – 3)= (x
2
+ x + 5)( x
2
+ x – 2)= (x
2
+ x + 5)(x + 2)(x – 1)
3.
Factorise (1 – x
2
)(1 – y
2
) + 4xy1 – x
2
– y
2
+ x
2
y
2
+ 4xy= 1 + x
2
y
2
+ 2xy – (x
2
+ y
2
– 2xy)= (1 + xy)
2
– (x – y)
2
= (1 + xy + x – y)(1 + xy – x + y)4.
Factorise 216 + 27b
3
+ 8c
3
– 108bc27b
3
+ 8c
3
+ 216 + 108bc=(3b)
3
+ (2c)
3
+ 6
3
+ 3.3b.2c.6 {a
3
+ b
3
+ c
3
– 3abc = (a + b + c)(a
2
+ b
2
+ c
2
– ab – bc– ca)}= (3b + 2c + 6)(9b
2
+ 4c
2
+ 36 – 6bc – 12c – 18b)
5.
Factorise (a
2
– b
2
)(a
2
+ ab + b
2
) – a
3
+ b
3
(a
2
– b
2
)(a
2
+ ab + b
2
)