Question

When does expanding and simplifying a(b + c) result in a positive value for ac?

Answer 1

Step-by-step explanation:(ab + bc)(ab + bc)

Simplifying

(ab + bc)(ab + bc)

Multiply (ab + bc) * (ab + bc)

(ab(ab + bc) + bc(ab + bc))

((ab * ab + bc * ab) + bc(ab + bc))

Reorder the terms:

((ab2c + a2b2) + bc(ab + bc))

((ab2c + a2b2) + bc(ab + bc))

(ab2c + a2b2 + (ab * bc + bc * bc))

(ab2c + a2b2 + (ab2c + b2c2))

Reorder the terms:

(ab2c + ab2c + a2b2 + b2c2)

Combine like terms: ab2c + ab2c = 2ab2c

(2ab2c + a2b2 + b2c2)

Answer 2

The expansion and simplification of algebra expression a(b + c) will have a positive value for ac when the arithmetic operation between a and b + c have the same sign i.e. either it is both positive or negative.

Expanding and simplifying algebra expression.

The expansion and simplification of algebra expression means a process of expressing the algebra expression in its simplest form.

The simplification of the expression a(b + c) can be expanded as:

ab + ac. This is because a and b + c is positive.

Also, assuming they are both negative, we have:

= -a(-b - c) (because - × - = +)

= +ab + ac

= ab + ac

Therefore, we can conclude that the expression a(b + c) will have a positive value for ac when the arithmetic operation between a and b + c have the same sign.