Question

How do you multiply $ (5y - 2)(5y + 2) $ ?

Answer 1

Hint: In this question we need to perform the multiplication of algebraic expressions. An algebraic expression consists of variables, exponents and constants. When we apply the mathematical operation multiplication on two or more algebraic expressions is called multiplication of algebraic expressions. For solving problems based on multiplication of algebraic expressions you must know to perform multiplication, division, addition and subtraction.

Complete step-by-step answer:
Let’s try to solve this question based on multiplication of algebraic multiplication. In multiplication of algebraic expression we will take each term of one algebraic expression and then multiply it by another algebraic expression. When we multiply two variables term then variables will multiply with each other and their coefficient will multiply with each other. For example let’s say we have to multiply $ 3x $ and $ 5x $ , so the multiplication will performed as follows both terms have $ x $ after multiplication it becomes $ {x^2} $ and from multiplication between $ 3 $ and $ 5 $ we get 15. So the multiplication of $ 3x $ and $ 5x $ we get $ 15{x^2} $ . Now, I assume that you have some idea of multiplication of variables. So let’s come back to our real problem.
Here we have to perform multiplication of $ (5y - 2)(5y + 2) $ .
 $ (5y - 2)(5y + 2) = 5y(5y + 2) - 2(5y + 2) $
 $ = 5y \times 5y + 5y \times 2 - (2 \times 5y) - (2 \times 2) $
 $ = (5 \times 5)(y \times y) + (5 \times 2)y - (5 \times 2)y - 2 \times 2 $
 $ = 25{y^2} + 10y - 10y - 4 $
 $ 10y - 10y = 0 $ .So it becomes
 $ (5y - 2)(5y + 2) = 25{y^2} - 4 $
Hence the value of $ (5y - 2)(5y + 2) $ after algebraic multiplication is $ 25{y^2} - 4 $ .
So, the correct answer is “ $ 25{y^2} - 4 $ ”.

Note: While performing multiplication of algebraic expressions be careful about the exponents of variables term most students make mistakes in this. From the above question you have seen that from multiplication of two linear algebraic expressions we have got a quadratic algebraic expression. Similarly, performing multiplication of algebraic expressions we get higher order algebraic expressions