Question

1. $9a + 8 - 2a - 3 - 5a$ 10. $4xy - 6xy + 5y - 9x$ 11. $7x + 2y + 5 - 5x + 9y - 1$ 12. $-5f - 7g + f - 5g - 4 + f$ 13. $-6 + 3a - b - 4a + 4b + 5$ 14. $6n^{2}-2n - 3 + 5n^{2}-9n - 6$ 15. $8c^{2}-c + 3 + 2c^{2}-c + 2$ 16. $-12x^{2}y - 3x^{2}y$ 17. $6a^{2}b^{2}+3ab^{2}-a^{2}b^{2}-4ab^{2}$ 18. $19x^{2}y - 4xy^{2}+5xy^{2}-16x^{2}y$ 19. write the perimeter of the rectangle as a simplified expression. 20. write the perimeter of the triangle as a simplified expression.

Explanation:

Step1: Combine like - terms for 9.

Combine the terms with 'a' and the constant terms: $(9a - 2a-5a)+(8 - 3)=2a + 5$

Step2: Combine like - terms for 10.

Combine the 'xy' terms: $(4xy-6xy)+5y - 9x=-2xy + 5y - 9x$

Step3: Combine like - terms for 11.

Combine the 'x' terms, 'y' terms and constant terms: $(7x-5x)+(2y + 9y)+(5 - 1)=2x+11y + 4$

Step4: Combine like - terms for 12.

Combine the 'f' terms and 'g' terms and the constant term: $(-5f + f+f)+(-7g-5g)-4=-3f-12g - 4$

Step5: Combine like - terms for 13.

Combine the 'a' terms, 'b' terms and constant terms: $(3a-4a)+(-b + 4b)+(-6 + 5)=-a + 3b-1$

Step6: Combine like - terms for 14.

Combine the $n^{2}$ terms, 'n' terms and constant terms: $(6n^{2}+5n^{2})+(-2n-9n)+(-3 - 6)=11n^{2}-11n - 9$

Step7: Combine like - terms for 15.

Combine the $c^{2}$ terms, 'c' terms and constant terms: $(8c^{2}+2c^{2})+(-c - c)+(3 + 2)=10c^{2}-2c + 5$

Step8: Combine like - terms for 16.

Combine the $x^{2}y$ terms: $(-12x^{2}y-3x^{2}y)=-15x^{2}y$

Step9: Combine like - terms for 17.

Combine the $a^{2}b^{2}$ terms and $ab^{2}$ terms: $(6a^{2}b^{2}-a^{2}b^{2})+(3ab^{2}-4ab^{2})=5a^{2}b^{2}-ab^{2}$

Step10: Combine like - terms for 18.

Combine the $x^{2}y$ terms and $xy^{2}$ terms: $(19x^{2}y-16x^{2}y)+(-4xy^{2}+5xy^{2})=3x^{2}y+xy^{2}$

Step11: Find the perimeter of the rectangle in 19.

The perimeter of a rectangle is $2(l + w)$. Here, $l = 7x + 1$ and $w=x - 3$.
$2((7x + 1)+(x - 3))=2(7x+1+x - 3)=2(8x - 2)=16x-4$

Step12: Find the perimeter of the triangle in 20.

The perimeter of a triangle is the sum of its side - lengths.
$(y - 4)+(3y + 5)+6y=y-4+3y + 5+6y=(y+3y+6y)+(-4 + 5)=10y + 1$

Answer:

1. $2a + 5$
2. $-2xy + 5y - 9x$
3. $2x+11y + 4$
4. $-3f-12g - 4$
5. $-a + 3b-1$
6. $11n^{2}-11n - 9$
7. $10c^{2}-2c + 5$
8. $-15x^{2}y$
9. $5a^{2}b^{2}-ab^{2}$
10. $3x^{2}y+xy^{2}$
11. $16x-4$
12. $10y + 1$