Question: Solve the following multiplication: (12x + 2y) (5x  4y)
Answer: Mathematics for class eight is really interesting and I feel that itâ€™s the first step in the journey of advanced mathematics. From now on the problems will be really very challenging to solve as it needs a lot of practice and in the same time there are lot of formulas to play with. My statement should not worry students, its always exciting to solve new and challenging problems.
Let us explore this question. In this question we need to multiply two binomials having two variables x and y. The two binomials are (12x + 2y) and (5x  4y). Let us multiply them and understand different steps in the multiplications: (12x + 2y) x (5x  4y)
In this case we will be multiply first term of first binomial with second binomial and add this value with the multiplication of second term of first binomial with the second binomial. See below steps:
(12x + 2y)(5x  4y)
= 12x (5x − 4y) + 2y(5x − 4y)
Multiplication symbol is not necessary to present between number and/or variable. Like multiplication symbol is not necessary to present between 12x and (5x − 4y)
Now the multiplication will follow the same rule we apply with two numbers. Let us multiply them:
12x (5x − 4y) + 2y(5x − 4y)
= 60x^{2} − 48xy + 10yx − 8y^{2}. Please note that xy and yx both are same
= 60x^{2} − 48xy + 10xy − 8y^{2}
= 60x^{2} − 38xy − 8y^{2} (this is the result)
