(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)slove this question fast

1.	(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)slove this question fast
Answer» Let's simplify step-by-step. $(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)$ Distribute: $\rightarrow (a)(c)+(a)(-d)+(b)(c)+(b)(-d)+(a)(c)+(a)(d)+(-b)(c)+(-b)(d)+(2)(ac)+(2)(bd)$ $\rightarrow ac+-ad+bc+-bd+ac+ad+-bc+-bd+2ac+2bd$ Combine Like Terms: $\rightarrow ac+-ad+bc+-bd+ac+ad+-bc+-bd+2ac+2bd$ $\rightarrow (ac+ac+2ac)+(-ad+ad)+(bc+-bc)+(-bd+-bd+2bd)$ $\rightarrow 4ac$ ∴ $(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)=4ac$ Additional Information :) What is an equation? A mathematical STATEMENT that says that two things are equal is known as an equation. What are the parts of equation? An equation consists of a variable, constants and coefficient. What is a Polynomial? An equation that can consist of constants, variables and exponents are known as Polynomial. What are Monomial, Binomial, TRINOMIAL? A monomial consists of 1 TERM. A binomial consists of 2 terms. A trinomial consists of 3 terms. What are like terms? Terms whose variables are equal are known as like terms.

Answer»

Let's simplify step-by-step.

$(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)$

Distribute:

$\rightarrow (a)(c)+(a)(-d)+(b)(c)+(b)(-d)+(a)(c)+(a)(d)+(-b)(c)+(-b)(d)+(2)(ac)+(2)(bd)$

$\rightarrow ac+-ad+bc+-bd+ac+ad+-bc+-bd+2ac+2bd$

Combine Like Terms:

$\rightarrow ac+-ad+bc+-bd+ac+ad+-bc+-bd+2ac+2bd$

$\rightarrow (ac+ac+2ac)+(-ad+ad)+(bc+-bc)+(-bd+-bd+2bd)$

$\rightarrow 4ac$

∴ $(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)=4ac$

Additional Information :)

What is an equation?

A mathematical STATEMENT that says that two things are equal is known as an equation.

What are the parts of equation?

An equation consists of a variable, constants and coefficient.

What is a Polynomial?

An equation that can consist of constants, variables and exponents are known as Polynomial.

What are Monomial, Binomial, TRINOMIAL?

A monomial consists of 1 TERM. A binomial consists of 2 terms. A trinomial consists of 3 terms.