Question

check if each of the following equalities is true for all value of the variables (1-2b)(1-5b+b^2)+(2b-1)(1-6b+b^2)=b(1-2b)

Answer 1

The check done confirmed that the equality is true since the value arrived at while solving the expression is same as the given value

How to check if the equalities is true for all value of the variables

Given data

$(1-2b)(1-5b+b^{2} )+(2b-1)(1-6b+b^{2} )=b(1-2b)$

breaking the expansion into 2 we have

$=(1-2b)(1-5b+b^{2} )$

$=(1)(1)+(1)(-5b)+(1)(b^2)+(-2b)(1)+(-2b)(-5b)+(-2b)(b^2)$

$=1-5b+b^2-2b+10b^2-2b^3$

$=-2b^3+11b^2-7b+1$

expanding this $(2b-1)(1-6b+b^2)$ gives:

$=2b^3-13b^2+8b-1$

adding both equation gives

$= -2b^3+11b^2-7b+1 + 2b^3-13b^2+8b-1$

$= -2b^2 + b$

$= b - 2b^2$

$= b (1 - 2b)$

Since the expansion gave same value we can say that the equality is true

Read more on equations here: brainly.com/question/13763238

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