Question

PLZ HELP NOW I REALLY NEED THIS WILL MARK BRAINLIEST TO PERSON WITH THE FIRST RIGHT ANSWER!!!!!
Replace * with a monomial to obtain an identity.

(*-2m)²=100-40m+4m²

Answer 1

Answer:

(2m + 1)(2m + 1) = 4m + 2

Simplifying

(2m + 1)(2m + 1) = 4m + 2

Reorder the terms:

(1 + 2m)(2m + 1) = 4m + 2

Reorder the terms:

(1 + 2m)(1 + 2m) = 4m + 2

Multiply (1 + 2m) * (1 + 2m)

(1(1 + 2m) + 2m * (1 + 2m)) = 4m + 2

((1 * 1 + 2m * 1) + 2m * (1 + 2m)) = 4m + 2

((1 + 2m) + 2m * (1 + 2m)) = 4m + 2

(1 + 2m + (1 * 2m + 2m * 2m)) = 4m + 2

(1 + 2m + (2m + 4m2)) = 4m + 2

Combine like terms: 2m + 2m = 4m

(1 + 4m + 4m2) = 4m + 2

Reorder the terms:

1 + 4m + 4m2 = 2 + 4m

Add '-4m' to each side of the equation.

1 + 4m + -4m + 4m2 = 2 + 4m + -4m

Combine like terms: 4m + -4m = 0

1 + 0 + 4m2 = 2 + 4m + -4m

1 + 4m2 = 2 + 4m + -4m

Combine like terms: 4m + -4m = 0

1 + 4m2 = 2 + 0

1 + 4m2 = 2

Solving

1 + 4m2 = 2

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + 4m2 = 2 + -1

Combine like terms: 1 + -1 = 0

0 + 4m2 = 2 + -1

4m2 = 2 + -1

Combine like terms: 2 + -1 = 1

4m2 = 1

Divide each side by '4'.

m2 = 0.25

Simplifying

m2 = 0.25

Reorder the terms:

-0.25 + m2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0

-0.25 + m2 = 0

Factor a difference between two squares.

(0.5 + m)(-0.5 + m) = 0

Subproblem 1

Set the factor '(0.5 + m)' equal to zero and attempt to solve:

Simplifying

0.5 + m = 0

Solving

0.5 + m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-0.5' to each side of the equation.

0.5 + -0.5 + m = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0

0 + m = 0 + -0.5

m = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5

m = -0.5

Simplifying

m = -0.5

Subproblem 2

Set the factor '(-0.5 + m)' equal to zero and attempt to solve:

Simplifying

-0.5 + m = 0

Solving

-0.5 + m = 0

Move all terms containing m to the left, all other terms to the right.

Add '0.5' to each side of the equation.

-0.5 + 0.5 + m = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0

0 + m = 0 + 0.5

m = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5

m = 0.5

Simplifying

m = 0.5

Solution

m = {-0.5, 0.5}

Equation: Variable:

(2m + 1)(2m + 1) = 4m + 2

Answer 2

$\huge{\underline{\bold{Solution:-}}}$

=> (-2m)²=100-40m+4m²

=> 4m² = 100-40m+4m²

=> 100-40m+4m²- 4m²=0

=> 100-40m=0

=> 100=40m

=> m = (100/40)

=> m=(5/2)

$\boxed{\bold{ =>m=2.5 }}$

Important Formulas:-

1. (-)ve × (-)ve = (+)ve
2. (-)ve × (+)ve = (-)ve

___________________

$\huge{\mathcal{ Be \: Brainy }}$