Use the direct method to evaluate the following products : (y + 5)(y – 3)

Use the direct method to evaluate the following products :
(y + 5)(y – 3)

Sum

(y + 5) (y – 3) = (y × y) + (y × −3) + (5 × y) + (5 × −3)

= y² + (−3y) + (5y) − 15

= y²− 3y + 5y − 15

= y² + 2y − 15

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Chapter 12 Identities
Exercise 12 (A) | Q 1.2 | Page 150

Evaluate the following using suitable identity:

(102)³

Write the expanded form:

`(-3x + y + z)^2`

Write in the expanded form (a² + b² + c² )²

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

Find the value of 64x³ − 125z³, if 4x − 5z = 16 and xz = 12.

If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`

If a² - 3a + 1 = 0, and a ≠ 0; find:

Evaluate the following without multiplying:
(999)²

Simplify:
(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)

Factorise the following:

9x² + 4y² + 16z² + 12xy – 16yz – 24xz