Find the values of a and b such that

x^2 + 2x - 7 = (x+a)^2 + b

The values of a and b are 1 and -8

Step-by-step explanation:

Let us solve the question by comparing the two sides.

∵ x² + 2x - 7 = (x + a)² + b

→ Let us solve the bracket on the right side

∵ (x + a)² = (x)(x) + 2(x)(a) + (a)(a)

∴ (x + a)² = x² + 2ax + a²

→ Substitute it in the right side above

∴ x² + 2x - 7 = x² + 2ax + a² + b

→ Compare the like terms on both sides (terms of x², terms of x

   and numerical terms)

∵ The terms of x are 2x and 2ax

→ Equate them

∵ 2x = 2ax

→ Divide both sides by 2x

∴ =

∴ 1 = a

∴ The value of a = 1

∵ The numerical terms are -7 and a² + b

→ Equate them

∵ -7 = a² + b

→ Substitute a by 1

∴ -7 = (1)² + b

∴ -7 = 1 + b

→ Subtract 1 from both sides

∵ -7 - 1 = 1 - 1 + b

∴ -8 = b

∴ The value of b = -8

∴ The values of a and b are 1 and -8

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".