Question

use suitable identity to solve the following 1)(4a+7c) 2) (32-4y) (32-4y) 3) (a+2b) (a-2b) 4) (7x+y) (7x+z)​

Answer 1

Q1)

[tex](4a + 7c)^2\\\\ Using (a+b)^2 = a^2 + b^2 + 2ab\\\\ (4a)^2 + (7c)^2 + 2(4a)(7c)\\ 16a^2 + 49c^2 + 56ac[/tex]

Q2)

[tex](32-4y)(32-4y) [/tex]

This can be represented as:

[tex](32-4y)^2\\\\ Using (a-b)^2 = a^2 + b^2 - 2ab\\\\ 32^2 + (4y)^2 -2(32)(4y)\\ 1024 + 16y^2 -256y[/tex]

Q3)

[tex](a+2b)(a-2b)\\\\ Using (a+b)(a-b) = a^2 - b^2\\\\ a^2 - (2b)^2\\ a^2 - 4b^2[/tex]

Q4)

[tex](7x + y)(7x+z)\\\\ Using (x+a)(x+b) = x^2 + (a+b)x + ab\\ (7x)^2 + (x +y)7x + (x*y)\\ 49x^2 + 7x^2 + 7xy + xy\\ 56x^2 + 8xy\\ [/tex]

Hope this helped!