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

#### MatthewSA

##### New member
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
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
.

#### MatthewSA

##### New member
Thank you! I understand now. #### Jomo

##### Elite Member
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
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