Advertisements
Advertisements
Question
Show that (x + 2y)2 – (x – 2y)2 = 8xy
Advertisements
Solution
L.H.S = (x + 2y)2 – (x – 2y)2
= x2 + (2 × x × 2y) + (2y)2 – [x2 – (2 × x × 2y) + (2y)2]
= x2 + 4xy + 4y2 – [x2 – 4xy + 22y2]
= x2 + 4xy + 4y2 – x2 + 4xy – 4y2
= x2 – x2 + 4xy + 4xy + 4y2 – 4y2
= x2(1 – 1) + xy(4 + 4) + y2(4 – 4)
= 0x2 + 8xy + 0y2
= 8xy
= R.H.S
∴ (x + 2y)2 – (x – 2y)2 = 8xy ...[∵ (a + b)2 = a2 + 2ab + b2 and (a – b)2 = a2 – 2ab + b2]
APPEARS IN
RELATED QUESTIONS
Find the following squares by suing the identities
(xy + 3z)2
Simplify (m2 − n2m)2 + 2m3n2
Use an expansion formula to find the value.
(102)2
Expand: (2a – 3b)2
Factorise the following expressions
x2 + 14x + 49
Factors of 9x2 + 6xy are
(a + b)2 – 2ab = ______ + ______.
Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2.
`x^2/4 + 2x + 4`
The area of a square is given by 4x2 + 12xy + 9y2. Find the side of the square.
The area of a circle is given by the expression πx2 + 6πx + 9π. Find the radius of the circle.
