Question

16x2-1/144 factorize​

Answer 1

Answer:

STEP

1

:

1

Simplify ———

144

Equation at the end of step

1

:

1

(16 • (x2)) - ———

144

STEP

2

:

Equation at the end of step

2

:

1

24x2 - ———

144

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 144 as the denominator :

24x2 24x2 • 144

24x2 = ———— = ——————————

1 144

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

24x2 • 144 - (1) 2304x2 - 1

———————————————— = ——————————

144 144

Trying to factor as a Difference of Squares:

3.3 Factoring: 2304x2 - 1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2304 is the square of 48

Check : 1 is the square of 1

Check : x2 is the square of x1

Factorization is : (48x + 1) • (48x - 1)

Final result :

(48x + 1) • (48x - 1)

—————————————————————

144

Answer 2

Step-by-step explanation:

STEP

1

:

1

Simplify ———

144

Equation at the end of step

1

:

1

(16 • (x2)) - ———

144

STEP

2

:

Equation at the end of step

2

:

1

24x2 - ———

144

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 144 as the denominator :

24x2 24x2 • 144

24x2 = ———— = ——————————

1 144