[[1]] is the product of 3x3y2and (2x−3y). Also, verify the result for x =−1,y = 2.

Question

[[1]] is the product of 3x3y2and (2x−3y). Also, verify the result for x =−1,y = 2.

Accepted Answer

Given: - The polynomials are 3x3y2and (2x−3y).
Before proceeding with the solution, first, we will understand the concept of the product of one monomial and one polynomial. We will consider one monomial, axy and one polynomial, (bx+cy). To find the product of the monomial and polynomial, we have to multiply each term of the second polynomial by the monomial. So, the product of the monomial and polynomial is given as,
axy×(bx+cy)=abx2y + acxy2
Now, coming to the question, we are asked for the product of 3x3y2 and (2x−3y). On multiplying the term, we get,
⇒3x3y2 × (2x−3y)) = 3x3y2×2x−3x3y2×3y
Multiply the terms,
⇒3x3y2 × (2x−3y)=6x4y2−9x3y3.
So, the product is 6x4y2−9x3y3.
Now substitute the value x=−1,y=2 in each expression and get the value.
For 3x3y2,
⇒3(−1) 3 (2) 2 ⇒3(−1) 3 (2) 2
Simplify the term,
⇒3×−1×4
Multiply the term,
⇒−12.................…… (1)
For (2x−3y),
⇒2×−1−3×2
Multiply the term,
⇒−2−6
Simplify the term,
⇒−8...............…… (2)
Now multiply equation (1) and (2),
⇒−12×−8=96................….. (3)
For 6x4y2−9x3y3,
⇒6(−1)4(2)2−9(−1)3(2)3
Simplify the term,
⇒6×1×4−9×−1×8
Multiply the term,
⇒24+72
Add the terms,
⇒96..................…… (4)
Now equate the equation (3) and equation (4),
⇒96=96
Hence, the product of 3x3y2and (2x−3y) is 6x4y2−9x3y3 and it is verified.

[[1]] is the product of 3x3y2and (2x−3y). Also, verify the result for x =−1,y = 2.

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