Question

Factorise:
(i) (x+y)(2a+b)+(x-y)(2a+b)
(ii) 9x²- 144y²
(iii) 6x² - 3x²y - bc² + 2c²​

Answer 1

(i)

.

(ii)

.

Factoring: x2 - 16y2

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 : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + 4y) • (x - 4y)

Final result :

9 • (x + 4y) • (x - 4y)

(iii)

$= > 6x² - 3x²y - bc² + 2c² \\ = > 3x(2x + 3) - 1(2x + 3) \\ = > (3x - 1)(2x + 3)$

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