Question

Fill proper terms in the following blanks.
(i) (x + 2y)² = x² + ____ + 4y2
(ii) (2x - 5y)² = ____ - 20xy + ____
(iii) (101)² = (100 + 1)² = ____ + ____ + 1² = ____
(iv) (98)² = (100 - 2)² = 10000 - ____ + ____ = ____
(v) (5m + 3n)(5m - 3n) = ____ - ____ = ____ - ____

Answer 1

Hi,

Problem:

Fill proper terms in the following blanks.

(i) (x + 2y)² = x² + ____ + 4y2

(ii) (2x - 5y)² = ____ - 20xy + ____

(iii) (101)² = (100 + 1)² = ____ + ____ + 1² = ____

(iv) (98)² = (100 - 2)² = 10000 - ____ + ____ = ____

(v) (5m + 3n)(5m - 3n) = ____ - ____ = ____ - ____

Solution:

(i) (x + 2y)² = x² + 2x(2y)+ 4y² = x² + 4xy + 4y²

∴$(x+y)^{2} = x^{2} +2xy+y^{2}$

(ii) (2x - 5y)² = 4x² - 20xy + 25y²

∴$(x-y)^{2} = x^{2} - 2xy+y^{2}$

(iii) (101)² = (100 + 1)² = (100)² + 2(100)(1)+ 1² = 10000+200+1 = 10201

∴ $(x+y)^{2} = x^{2} +2xy+y^{2}$

(iv) (98)² = (100 - 2)² = 10000 - 2(2)(100) +(2)² = 10000-400+4 =9604

∴ $(x-y)^{2} = x^{2} - 2xy+y^{2}$

(v) (5m + 3n)(5m - 3n) = (5m)² - (3n)² = 25 m² - 9n²

∴ (a+b)(a-b) = $a^{2} - b^{2}$

hope it helps you.

Answer 2

The following problem can be easily solved as shown below:

(i) (x + 2y)² = x² + 4xy + 4y²

(ii) (2x - 5y)² = 4x² - 20xy + 25y²

(iii) (101)² = (100 + 1)² = 10000 + 200 + 1² = 10201

(iv) (98)² = (100 - 2)² = 10000 - 400 + 4 = 9604

(v) (5m + 3n)(5m - 3n) = ____ - ____ = ____ - ____