Question

5a^2 - 5b^2=.....................​

Answer 1

Answer:

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Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(5 • (a2)) - 5b2

STEP

2

:

Equation at the end of step

2

:

5a2 - 5b2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

5a2 - 5b2 = 5 • (a2 - b2)

Trying to factor as a Difference of Squares:

4.2 Factoring: a2 - b2

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 : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Final result :

5 • (a + b) • (a - b)

Answer 2

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5a² - 5b² = ?

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5a² - 5b² = 5(a² - b²)