3. Multiply the following and verify the result for x = 2, y = 1, and z = 3.

(a) 6yz × (x²y² + 2yz)
(b) 9x²(2x³ - 5x²)
(c) (3/2)x(10y²x - 100yx²)

We multiplied each expression and substituted the values to find the results: (a) = 126, (b) = -144, (c) = -1140. The calculations were completed step-by-step for clarity. Each expression was expanded before substituting the values of x, y, and z.
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Answered by Anonymous | 2025-07-04

Let's address each part of the question step-by-step:
(a) Multiply :
Given expression: 6 yz × ( x 2 y 2 + 2 yz )
First, distribute 6 yz to each term inside the parentheses:
6 yz × ( x 2 y 2 ) = 6 x 2 y 3 z
6 yz × ( 2 yz ) = 12 y 2 z 2
The resulting expression is:
6 x 2 y 3 z + 12 y 2 z 2
Verify at x = 2 , y = 1 , z = 3 :
First term: 6 ( 2 ) 2 ( 1 ) 3 ( 3 ) = 72
Second term: 12 ( 1 ) 2 ( 3 ) 2 = 108
Adding them, the sum is 72 + 108 = 180 .
(b) Multiply :
Given expression: 9 x 2 ( 2 x 3 − 5 x 2 )
Distribute 9 x 2 to each term inside the parentheses:
9 x 2 × ( 2 x 3 ) = 18 x 5
9 x 2 × ( − 5 x 2 ) = − 45 x 4
The resulting expression is:
18 x 5 − 45 x 4
Verify at x = 2 :
First term: 18 ( 2 ) 5 = 576
Second term: − 45 ( 2 ) 4 = − 720
Adding them, the sum is 576 − 720 = − 144 .
(c) Multiply :
Given expression: 2 3 ​ x ( 10 y 2 x − 100 y x 2 )
Distribute 2 3 ​ x to each term inside the parentheses:
2 3 ​ x × ( 10 y 2 x ) = 15 x y 2 x 2 = 15 x 3 y 2
2 3 ​ x × ( − 100 y x 2 ) = − 150 x y x 3 = − 150 x 4 y
The resulting expression is:
15 x 3 y 2 − 150 x 4 y
Verify at x = 2 , y = 1 :
First term: 15 ( 2 ) 3 ( 1 ) 2 = 120
Second term: − 150 ( 2 ) 4 ( 1 ) = − 2400
Adding them, the sum is 120 − 2400 = − 2280 .

Answered by LucasMatthewHarris | 2025-07-06