Question

expand (1/4 a - 1/2 b+1)^2

Answer 1

Answer:

The expanded form is $(\frac{1}{4}a - \frac{1}{2}b + 1)^{2}$ = $\frac{1}{16}a^{2} - \frac{1}{4}b^{2} + 1 - \frac{1}{4}ab - b + \frac{1}{2}a$

Step-by-step explanation:

Given: Expression

To find: Using suitable identity and expand?

Solution:

Using algebraic identity,

$(x+y+z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz +2zx$

Here, $x = \frac{1}{4}a, y = \frac{1}{2}b, z = 1$

$(\frac{1}{4}a-\frac{1}{2}b+1)^2=(\frac{1}{4}a)^2+(-\frac{1}{2}b)^2+1^2+2\times (\frac{1}{4}a)\times (-\frac{1}{2}b)+2\times (-\frac{1}{2}b)\times 1+2\times (\frac{1}{4}a)\times 1$

$(\frac{1}{4}a-\frac{1}{2}b+1)^2=\frac{1}{16}a^2+\frac{1}{4}b^2+1-\frac{1}{4}ab-b+\frac{1}{2}a$

Therefore, the expanded form is

$(\frac{1}{4}a-\frac{1}{2}b+1)^2=\frac{1}{16}a^2+\frac{1}{4}b^2+1-\frac{1}{2}ab-b+\frac{1}{2}a$

hope it help.