Question

State whether the following expression is perfect square:4m^2+4m+1

Answer 1

Answer:

answer given below

Step-by-step explanation:

Step by step solution :

STEP

1

:

Equation at the end of step 1

(22m2 - 4m) + 1 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 4m2-4m+1

The first term is, 4m2 its coefficient is 4 .

The middle term is, -4m its coefficient is -4 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 4 • 1 = 4

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4 .

-4 + -1 = -5

-2 + -2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2

4m2 - 2m - 2m - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

2m • (2m-1)

Add up the last 2 terms, pulling out common factors :

1 • (2m-1)

Step-5 : Add up the four terms of step 4 :

(2m-1) • (2m-1)

Which is the desired factorization

Multiplying Exponential Expressions:

2.2 Multiply (2m-1) by (2m-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2m-1) and the exponents are :

1 , as (2m-1) is the same number as (2m-1)1

and 1 , as (2m-1) is the same number as (2m-1)1

The product is therefore, (2m-1)(1+1) = (2m-1)2

Equation at the end of step

2

:

(2m - 1)2 = 0

STEP

3

:

Solving a Single Variable Equation

3.1 Solve : (2m-1)2 = 0

(2m-1) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 2m-1 = 0

Add 1 to both sides of the equation :

2m = 1

Divide both sides of the equation by 2:

m = 1/2 = 0.500

Supplement : Solving Quadratic Equation Directly

Solving 4m2-4m+1 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

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