Ab-a-b+1 I know it splits into a(b-1)-1(b-1) but can someone explain in words how it becomes (a-1)(b-1) thanks

ab - a - b + 1 = (a - 1)(b - 1)

Step-by-step explanation:

Let us explain factorization by grouping

In the expression of 4 terms ax + by + bx + ay

Take every two terms have a common factor in a bracket

Take the common factor out of the brackets

Take the bracket as a common factor

Let us do these steps with our question

∵ ab - a - b + 1 is an expression of 4 terms

→ Take ab and a in a bracket, -b and 1 in another bracket

∴ ab - a - b + 1 = (ab - a) + (-b + 1)

→ Take a as a common factor from the 1st bracket and -1 from

   the 2nd bracket

∴ (ab - a) + (-b + 1) = a(b -1) + -1(b - 1)

→ Take the bracket (b - 1) as a common factor

∴ a(b -1) + -1(b - 1) = (b - 1)(a + -1)

∵ (+)(-) = (-)

∴ (b - 1)(a + -1) = (b - 1)(a -1)

→ Change the order of the bracket

∴ (b - 1)(a -1) = (a - 1)(b - 1)

∴ ab - a - b + 1 = (a - 1)(b - 1)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: 7270

step-by-step explanation: