Question

36. Factorization of the polynomial
(x - y)²a² + 2(x - y) (x + y)ab + (x + y)²b² gives
(a) (ax - by) (ax + by)
(b) (ax + by) (bx + ay)
(c) (ax - ay + bx + by)²
(d) (ax + ay + bx + by)²

How that answer come plz tell ​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

We have to factorise the given polynomial.

= (x - y)²a² + 2(x - y)(x + y)ab + (x + y)²b² ★

We know that:

→ (p + q)² = p² + 2pq + q²

Now, let us assume that:

→ p = a(x - y)

→ q = b(x + y)

Therefore, we can write the above polynomial as:

= [a(x - y)]² + 2 × [a(x - y)] × [b(x + y)] + [b(x + y)]²

= p² + 2pq + q²

= (p + q)²

Now substituting the values in the expression, we get:

= (ax - ay + bx + by)²

★ Which is the factorisation of the given polynomial.

$\textsf{\large{\underline{More To Know}:}}$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab