Question

ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?

Answer 1

Explained below.

Explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

`[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z`

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

`[(x^(2) + 3y^(2) - 6xy)+(2x^(2) - y^(2) + 8xy)+(y^(2) + 8)+(x^(2) - 3xy)] - [-3x^(2) + 4y^(2) - xy + x - y + 3]\\=[x^(2) + 3y^(2) - 6xy+2x^(2) - y^(2) + 8xy+y^(2) + 8+x^(2) - 3xy]- [-3x^(2) + 4y^(2) - xy + x - y + 3]\\=[4x^(2)+3y^(2)-xy+8]-[-3x^(2) + 4y^(2) - xy + x - y + 3]\\=4x^(2)+3y^(2)-xy+8+3x^(2)-4y^(2)+xy-x+y-3\\=7x^(2)-y^(2)-x+y+5`

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

`A=(x^(2) - xy + y^(2) - x + y + 3) - (-x^(2)+ 3y^(2)- 4xy + 1)\\=x^(2) - xy + y^(2) - x + y + 3 +x^(2)- 3y^(2)+ 4xy -1\\=2x^(2)-2y^(2)+3xy-x+y+2`

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

`A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7`

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

`A=(2x^(2) - 3y^(2) + xy)-(x^(2) - 2xy + 3y^(2))\\=2x^(2) - 3y^(2) + xy-x^(2) + 2xy - 3y^(2)\\=x^(2)-6y^(2)+3xy`

Thus, the expression is (x² - 6y² + 3xy).