Simplify by Using Formula : (X + Y - 3) (X + Y + 3) - Mathematics

Simplify by using formula :
(x + y - 3) (x + y + 3)

Sum

(x + y - 3) (x + y + 3)
= (x + y)² - (3)²
= x² + y² + 2xy - 9
(Using identity : (a + b)(a - b) = a² - b²).

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Chapter 4: Expansions - Exercise 4.1

Chapter 4 Expansions
Exercise 4.1 | Q 4.4

Evaluate the following using suitable identity:

(102)³

Evaluate following using identities:

991 ☓ 1009

If 2x+3y = 13 and xy = 6, find the value of 8x³ + 27y³

Find the value of 27x³ + 8y³, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]

If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`

Use the direct method to evaluate :
(xy+4) (xy−4)

If a² + b² + c² = 41 and a + b + c = 9; find ab + bc + ca.

Expand the following:

(4a – b + 2c)²

Factorise the following:

25x² + 16y² + 4z² – 40xy + 16yz – 20xz

Prove that (a + b + c)³ – a³ – b³– c³ = 3(a + b)(b + c)(c + a).