Question

find the product
(2xy+3x)(4x^2y^2-6xyz+9z^2)​

Answer 1

Step-by-step explanation:

Given find the product

(2xy+3x)(4x^2y^2-6xyz+9z^2)

• We need to find the product of the given algebraic expression.
• So we need to multiply each term with the other term
• So (2xy + 3x) (4x^2y^2 – 6 xyz + 9 z^2)
• So 2xy x 4x^2y^2 – 2xy x 6xyz + 2xy x 9z^2 + 3x x 4x^2y^2 – 3x x 6 xyz + 3x x 9z^2
• = 8x^3y^3 – 12 x^2y^2 z + 18 xyz^2 + 12x^3y^2 – 18 x^2yz + 27xz^2

• If the question is (2x – y + 3z)(4x^2 + y^2 + 9z^2 + 2xy + 3yz – 6xz)
• This is in the form of a^3 + b^3 + c^3 – 3abc
•                                    2x^3 + (-y)^3 + 3z^3 - 3(2x)(-y)(3z)
•                                  2x^3 - y^3 + 3z^3 + 18 xyz

Reference link will be

https://brainly.in/question/3955351

Answer 2

Given : (2xy+3z)(4x²y²-6xyz+9z²)​

To find : Product

Solution:

Correct Question is

(2xy+3z)(4x²y²-6xyz+9z²)​

= (2xy+3z)( (2xy)²-2xy*3z+ (3z)²)​

using (a + b) (a² - ab + b²) = a³ + b³

a = 2xy

b = 3z

= (2xy)³ + (3z)³

= 8x³y³  + 27z³

(2xy+3z)(4x²y²-6xyz+9z²)​  = 8x³y³  + 27z³

Direct multiplication method

(2xy+3z)(4x²y²-6xyz+9z²)​

= 2xy(4x²y²-6xyz+9z²)​ + 3z(4x²y²-6xyz+9z²)​

= 8x³y³  - 12x²y²z + 18xyz²   + 12x²y²z  - 18xyz²  + 27z³

=  8x³y³  + 27z³

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