Question

Factorise each of the following polynomial using ( a + b )² = a² + 2ab + b² and ( a - b)² = a² - 2ab + b².

a) x² + 6xy + 9y²

b) ( a + b)² - 4ab

c) ( 3x - 5y)² + 2 (3x - 5y) ( 2y - x) + (2y - x)²

d) 25p² - 50pq + 25q² ​

Answer 1

Answer:

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Answer 2

EVALUATION★

(a)

$= x {}^{2} + 6xy + 9y {}^{2}$

• can be this written as

• $x {}^{2} + (3y ){}^{2} + 2(x)(3y)$
• we know that

• $= > a {}^{2} + b {}^{2} + 2ab = (a + b) {}^{2}$

$\\ \\ = (x + 3y) {}^{2}$

• =====================================

(b)

• ( a + b)² - 4ab

• we know that

• $= > (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

• $= a { }^{2} + b {}^{2} + 2ab - 4ab \\ \\ = a {}^{2} + b {}^{2} - 2ab$

• we know that

• $= > a {}^{2} + b {}^{2} - 2ab = (a - b) {}^{2}$

$= (a - b) {}^{2}$

• ====================================

(c)

• ( 3x - 5y)² + 2 (3x - 5y) ( 2y - x) + (2y - x)²

• we know that

$= > a {}^{2} + b {}^{2} + 2ab = (a + b) {}^{2}$

$(3x - 5y + 2y - x) {}^{2} \\ \\ \\ or \: \\ = (2x - 3y) {}^{2}$

===========================================

(d)

• 25p² - 50pq + 25q²

• can be this written as

• $= (5p) {}^{2} + (5q) {}^{2} - 2(5p)(5q)$

• we know that

• $= > a {}^{2} + b {}^{2} - 2ab =( a - b) {}^{2}$

$= (5p - 5q) {}^{2}$

• ===============================

I hope it helps you