Solve: Adding and Subtracting Polymonials

Add: (–6 – n + 2n2) + (8 – 3n – 10n2)
A. –2 – 4n – 8n2
B. 2 – 2n – 8n2
C. 2 – 4n – 8n2
D. –2 – 2n – 8n2

Add: (8x + 2y – 3z – 4) + (–4x – 5y + 4z + 6)
A. –4x + 3y – z + 2
B. 4x – 3y – z + 2
C. –4x + 3y –z – 2
D. 4x – 3y + z + 2

Subtract and simplify: (2p^2q – 3pq^2 + q^3) – (p^2q + q^3)
A. p^2q – 3pq^2
B. 2p^2q – 3pq^2
C. p^2q – 3pq^2+2q^3
D. p^2q – 2pq^2

Subtract and simplify: (–y^2 – 3y – 5) – (–3y^2 – 7y + 4)
A. 2y^2 – 10y + 4
B. 2y^2 + 4y – 9
C. –2y^2 – 10y – 1
D. 2y^2 – 7y – 9

Subtract and simplify: (10x^4 – 2x + 7) – (6x^4 + 2x^3 – 4x^2 – 1)
A. 4x^4 – 2x^3 + 4x^2 – 2x + 6
B. 4x^4 + 2x^3 – 4x^2 – 2x + 8
C. 4x^4 – 2x^3 + 4x^2 – 2x + 8
D. 16x^4 + 2x^3 + 4x^2 – 2x + 8

\( Add:\\ \\ (-6-n + 2n^2) + (8 - 3n - 10n^2) =\\ \\= -6-n + 2n^2 + 8 - 3n - 10n^2 =\\ \\=2 - 4n -8n^2 \\ \\ Answer : \ C. \ \ \2 - 4n - 8n2 \)


\( Add: \\ \\ (8x + 2y - 3z -4) + (-4x - 5y + 4z + 6) = \\ \\ =8x + 2y - 3z -4 -4x - 5y + 4z + 6=\\ \\=4 x - 3 y + z + 2 \\ \\ Answer : \ D. \ \ \ 4x - 3y + z + 2 \)


\( Subtract \ and \ simplify: \\\\ (2p^2q - 3pq^2 + q^3) -(p^2q + q^3)=\\ \\= 2p^2q - 3pq^2 + q^3 - p^2q -q^3 = \\ \\= p^2q - 3pq^2 \\ \\ Answer : \ A. \ \ \ \ p^2q - 3pq^2 \)


\( Subtract \ and \ simplify: \\\\ (-y^2 - 3y-5) - (-3y^2 - 7y + 4)= \\ \\= -y^2 - 3y-5+3y^2 +7y- 4 =\\ \\=2y^2+4y-9 \\ \\Answer : \ B. \ \ \ \ 2y^2 + 4y - 9 \)


\( Subtract \ and \ simplify: \\\\ (10x^4 -2x + 7)-(6x^4 + 2x^3 -4x^2 - 1) = \\ \\ = 10x^4 -2x + 7 - 6x^4 - 2x^3 +4x^2 + 1=\\ \\=4x^4 -2x^3 +4x^2-2x + 8 \\ \\Answer : \ C. \ \ \ \4x^4 -2x^3 + 4x^2- 2x + 8 \)
 

\( 1)\\(-6-n + 2n^2) + (8-3n-10n^2) =2-4n-8n^2\ \ \ \Rightarrow\ \ \ Ans. \ C\\\\2)\\(8x+2y-3z-4)+(-4x-5y+4z+6)=4x-3y+z+2\ \Rightarrow\ Ans. D\\\\3)\\(2p^2q-3pq^2+q^3)-(p^2q + q^3) =p^2q-3pq^2\ \ \ \Rightarrow\ \ \ Ans. \ A\\\\4)\\ (-y^2-3y-5)-(-3y^2-7y + 4) =-y^2-3y-5+3y^2+7y - 4=\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2y^2+4y-9\ \ \ \Rightarrow\ \ \ Ans. \ B\\ \)

\( 5)\\(10x^4-2x + 7)-(6x^4 + 2x^3-4x^2-1) =\\=10x^4-2x + 7-6x^4 - 2x^3+4x^2+1=\\=4x^4-2x^3+4x^2-2x+8\ \ \ \Rightarrow\ \ \ Ans. \ C \)


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