stumped by this problem ("expansion of products"): given (x+b)(x-1)=x2+3x-4, find "b"

MatthewSA

New member
Joined
Mar 16, 2018
Messages
2
stumped by this problem ("expansion of products"): given (x+b)(x-1)=x2+3x-4, find "b"

Question is find the value of 'b' in the equation: (x+b)(x-1)=x2+3x-4
I reduced the equation as follows:
  • x2-x+bx-b=x2+3x-4
  • x2-x+bx-b=x2+3x-4
  • bx-b=2x-4
I cant reduce it further to find the value of 'b'.

The answer key says that it is 4, as does wolfram alpha - but neither offer a step by step solution.

I am just starting with maths as an adult in order to rewrite my High School levels. I never took it past the early years of high school and not till the end.

Would appreciate a hint as to where to read up, or what the name of the problem is...

Thanks
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,134
Question is find the value of 'b' in the equation: (x+b)(x-1)=x2+3x-4
I reduced the equation as follows:
  • x2-x+bx-b=x2+3x-4
  • x2-x+bx-b=x2+3x-4 → x2 + x(-1+b) - b = x2 + 3x - 4

    Equating coefficients of same power of 'x', we get:

    equating coefficients of 'x'

    -1 + b = 3 → b = 4

    equating the constant terms (coefficients of x0) we get the same result.

  • bx-b=2x-4
I cant reduce it further to find the value of 'b'.

The answer key says that it is 4, as does wolfram alpha - but neither offer a step by step solution.

I am just starting with maths as an adult in order to rewrite my High School levels. I never took it past the early years of high school and not till the end.

Would appreciate a hint as to where to read up, or what the name of the problem is...

Thanks
.
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
2,984
Question is find the value of 'b' in the equation: (x+b)(x-1)=x2+3x-4
I reduced the equation as follows:
  • x2-x+bx-b=x2+3x-4
  • x2-x+bx-b=x2+3x-4
  • bx-b=2x-4
I cant reduce it further to find the value of 'b'.

The answer key says that it is 4, as does wolfram alpha - but neither offer a step by step solution.

I am just starting with maths as an adult in order to rewrite my High School levels. I never took it past the early years of high school and not till the end.

Would appreciate a hint as to where to read up, or what the name of the problem is...

Thanks
assuming that the value of b exists, then the easiest way to do this problem is to equate the constants. On the lhs the constant is -b and on the rhs the constant is -4. So -b= -4 or b=4
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
2,984
Question is find the value of 'b' in the equation: (x+b)(x-1)=x2+3x-4
I reduced the equation as follows:
  • x2-x+bx-b=x2+3x-4
  • x2-x+bx-b=x2+3x-4
  • bx-b=2x-4
I cant reduce it further to find the value of 'b'.

The answer key says that it is 4, as does wolfram alpha - but neither offer a step by step solution.

I am just starting with maths as an adult in order to rewrite my High School levels. I never took it past the early years of high school and not till the end.

Would appreciate a hint as to where to read up, or what the name of the problem is...

Thanks
When you bring the -x to the other side, this other side will have 4x, not 2 x
 
Top