Expand the Following: (A + 3b)2 - Mathematics

Expand the following:
(a + 3b)²

Sum

Using (x + y)²
= x² + 2xy + y², we get
(a + 3b)²
= a²+ 2(a)(3b) + (3b)²
= a² + 6ab + 9ab².

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Chapter 4: Expansions - Exercise 4.1

Chapter 4 Expansions
Exercise 4.1 | Q 2.1

Use suitable identity to find the following product:

`(y^2+3/2)(y^2-3/2)`

Evaluate the following using suitable identity:

(99)³

If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c².

Find the cube of the following binomials expression :

\[\frac{1}{x} + \frac{y}{3}\]

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

Find the following product:

\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]

If p + q = 8 and p - q = 4, find:
pq

Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)

Find the following product:

(x² – 1)(x⁴ + x² + 1)

Give possible expressions for the length and breadth of the rectangle whose area is given by 4a² + 4a – 3.