Question

factorise 400m^2-289n^2

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Answer 1

Step-by-step explanation:

400×m×m - 289×n×n

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Answer 2

Answer:

EP

1

:

Equation at the end of step 1

(400 • (m2)) - 172n2

STEP

2

:

Equation at the end of step

2

:

(24•52m2) - 172n2

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 400m2-289n2

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 : 400 is the square of 20

Check : 289 is the square of 17

Check : m2 is the square of m1

Check : n2 is the square of n1

Factorization is : (20m + 17n) • (20m - 17n)

Final result :

(20m + 17n) • (20m - 17n)