Question

(a) What should be subtracted from 3X² - 4Y² + 5XY + 20 to optain -X² - Y² + 6XY + 20?

(b) Find the final expression when the algebraic expression X² + 2XY + Y² is multiplied by XY.​

Answer 1

(1) What should be subtracted from 3X² - 4Y² + 5XY + 20 to optain -X² - Y² + 6XY + 20?

ⓈⓄⓁⓊⓉⒾⓄⓃ:--

Let Q be the expression to be subtracted.

Then according to the question,

3X² - 4Y² + 5XY + 20 - Q= -X² - Y² + 6XY + 20

---> Q= 3X² - 4Y² + 5XY + 20 - (-X² - Y² - 6XY - 20)

---> Q= 3X² - 4Y² + 5XY + 20 + X² + Y² - 6XY - 20

---> Q= 3X² + X² - 4Y² + Y² + 5XY + 6XY + 20 - 20

---> Q= 4X² - 3Y² - XY + 0

Hence, 4X² - 3Y² - XY should be subtracted from 3X² - 4Y² + 5XY + 20 to optain -X² - Y² + 6XY + 20.

(2) Find the final expression when the algebraic expression X² + 2XY + Y² is multiplied by XY.

ⓈⓄⓁⓊⓉⒾⓄⓃ:--

As per question:

X² + 2XY + Y² is multiplied by XY.

So, XY × X² + 2XY + Y².

= XY × X² + XY × 2XY + XY × Y²

= X² + ¹Y + 2X¹ + ¹Y + ¹ + XY¹ + 2

Therefore, a^m × a^n = a^m + ^n

= X³Y + 2X²Y² + XY³.

ⒽⓄⓅⒺ ⒾⓉ ⒾⓈ ⒽⒺⓁⓅⒻⓊⓁ

Answer 2

ⒽⒺⓎ

ⒽⒺⓇⒺ ⒾⓈ ⓎⓄⓊⓇ ⒶⓌⓃⓈⓌⒺⓇ

ⓆⓊⒺⓈⓉⒾⓄⓃ:

(a) What should be subtracted from 3X² - 4Y² + 5XY + 20 to optain -X² - Y² + 6XY + 20?

ⓈⓄⓁⓊⓉⒾⓄⓃ:--

Let Q be the expression to be subtracted.

Then according to the question,

3X² - 4Y² + 5XY + 20 - Q = -X² - Y² + 6XY + 20

----> Q = 3X² - 4Y² + 5XY + 20 - (-X² - Y² + 6XY + 20)

----> Q = 3X² - 4Y² + 5XY + 20 + X² + Y² - 6XY - 20

----> Q = 3X² + X² - 4Y² + Y² + 5XY - 6XY + 20 - 20

----> Q = 4X² - 3Y² - XY + 0

Hence,

4X² - 3Y² - XY should be subtracted from 3X² - 4Y² + 5 XY + 20 to obtain -X² - Y² + 6XY + 20.

ⓆⓊⒺⓈⓉⒾⓄⓃ:

(b) Find the final expression when the algebraic expression X² + 2XY + Y² is multiplied by XY.

ⓈⓄⓁⓊⓉⒾⓄⓃ:--

As per question:

X² + 2XY + Y² is multiplied by XY.

So, XY × X² + 2XY + Y²

= XY × X² + XY × 2XY + XY × Y²

= X² + ¹Y + 2X¹ + ¹Y¹ + ¹ + XY¹ + ²

Therefore, a^m × a^n = a^m + ^n

= X³Y + 2X²Y² + XY³

ⒽⓄⓅⒺ ⒾⓉ ⒽⒺⓁⓅⓈ