Algebraic Expressions Product

An expression is the important topic in algebra. Algebraic expression product  is the combination of variables and constants with basic arithmetic operators, they are add, subtract and then divide and multiplication.  For Example (p-9) is the algebraic expression.  Here p is the variable and 9 is the constant value and then ‘-‘is the subtraction operation.  In algebraic expressions product we can multiply the two algebraic expressions.
General Process of Algebraic Expressions Product

General process of algebraic expressions product: Now we have to assume the algebraic expressions (fx + gy) and (ax +by). This contains the below steps. They are,

Step 1: First we have to take multiplication of first term of the first expression with second expression. That is fx (ax+ by).

Step 2: Now we have to multiply the inner term values. That is fx(ax) +fx(by). It gives afx2 +bfxy

Step 3: Now we have to take multiplication of Second term of the first expression with second expression. That is gy (ax+ by) .

Step 4: Now we have to multiply the inner term values. That is gy(ax) +gy(by). It gives agxy +bgy2

Step 5: No we have to add the step 2 and step 4 values. That is afx2 +bfxy + agxy +bgy2

Step 6: Take the common terms we can get, afx2 + xy(bf + ag) +bgy2

This is the general rule of algebraic expressions product.
Problems Using the Algebraic Expressions Product

Problems 1 : Take algebraic expressions product of (j + 5) and (k− 6)

Solution: multiply the two given algebraic expressions

(j + 5)(k− 6)

= j(k − 6) + 5(k − 6)

= jk – 6j + 5k − 30

Problems 2 : Take algebraic expressions product of (2u +8)(u2− 2u − 10)

Solution: multiply the two given algebraic expressions

(2u +8)(u2− 2u − 10)

= (2u) (u2− 2u − 10) + (8) (u2− 2u − 10)

= (2u3 – 4u2 – 20u) + (8u2 – 16u − 80)

= 2u3 + 4u2 – 36u − 80