Question

Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b)

Answer 1

$(a+b)(5a-3b)+(a-3b)(a-b)$

Distribute:

⇒$(a)(5a)+(a)(-3b)+(b)(5a)+(b)(-3b)+(a)(a)+(a)(-b)+(-3b)(a)+(-3b)(-b)$

⇒ $5a^{2}+-3ab+5ab+-3b^{2}+a^{2}+-ab+-3ab+3b^{2}$

Combine Like Terms:

⇒ $5a^{2}+-3ab+5ab+-3b^{2}+a^{2}+-ab+-3ab+3b^{2}$

⇒ $(5a^{2}+a^{2})+(-3ab+5ab+-ab+-3ab)+(-3b^{2}+3b^{2})$

⇒ $6a^{2}+-2ab$

∴ After we simply the expression ⇒ $(a+b)(5a-3b)+(a-3b)(a-b)$ we get the answer as $6a^{2}+-2ab$

Additional Information :)

What is an expression?

When number and operations are grouped together to show the value of something they are known as expressions.

What are variables?

Variables are symbols or alphabets whose values can vary.

What are constants?

Constants are numbers whose values don't vary meaning they have a proper value.

What is an equation?

An operation that says two things are equal is known as an equation.

Types of equation?

There are five types of equations. They are -

• Quadratic Equation
• Linear Equation
• Radical Equation
• Exponential Equation
• Rational Equation

Types of expression?

There are five types of expressions. They are -

• Monomial
• Binomial
• Trinomial
• Polynomial
• Multinomial