Question

factorise 4a^7b-36a^5b^3​

Answer 1

4a7b - 36a5b3 = 4a5b • (a2 - 9b2)

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 : 9 is the square of 3

Check : a2 is the square of a1

Check : b2 is the square of b1

4a5b • (a + 3b) • (a - 3b)

Answer 2

Process:-

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

A2 - B2Note : AB = BA is the commutative property of multiplication.

A2 - B2Note : AB = BA is the commutative property of multiplication.Note : - AB + AB equals zero and is therefore eliminated from the expression.

Important points:-

Check : 9 is the square of 3

Check : 9 is the square of 3Check : a2 is the square of a1

Check : 9 is the square of 3Check : a2 is the square of a1Check : b2 is the square of b1

Answer:-

4a5b • (a + 3b) • (a - 3b)