Q1 of 65 Page 145

Let us factorise the following algebraic expressions:

(a – 1)x2 + a2xy + (a + 1)y2

Let p = (a – 1) and q = (a+1)


As we know that, a2 – b2 = (a – b)(a + b)


⇒ pq = a2 + 1


The given expression can be rewritten as:


px2 + pqxy + pq + qy2


⇒ px(x + qy) + y(x + qy)


⇒ (px + y)(x + qy)


On substituting the value of p and q, we get,


(ax – x + y)(x + ay + y)


More from this chapter

All 65 →
1

Let us factorise the following algebraic expressions:

(x2 – 1)2 + 8x(x2 + 1) + 19x2

 1

Let us factorise the following algebraic expressions:

(a – 1)x2 – x – (a – 2)

 1

Let us factorise the following algebraic expressions:

x2 – qx – p2 + 5pq – 6q2

 1

Let us factorise the following algebraic expressions: