Question

6 simplify
a) 2a - 4b + 8a + 2b
b) 7x + 3y - 3x + 4y
c) 9m - 2n + 7n + 2m
d) 9p - 7 + 6p - 5
e) 8r - 10 - 5s + 2
f) 12 - 6p - 5q + 3
g) 9k + 6m - 7k - 4n
h) 3m - 5m + 9k - 7k
i) x + 7y - 5y + 2x
j) 10t + 2w - 11t - 6w
k) 5ab - 4bc + 2ab + 3bc
l) 6mn - 3m + 4mn - 5m
m) 6 - 4kl - 9 - 5kl
n) 7x² + 6x - 6x² - 9x
o) 9p - 6q² + 5q² - 7q
p) 7 + 4h - 10h - 16
7 simplify the following
a) 5xy - 2yx
b) 4ab - 10ba + a
c) -2mn + 8nm + 6
d) 10 - ab - 5ab
e) 5m² + 7m + 3 - 2m² - 5m
f) 6a² + 9a - 1 + 5a² - 10a
g) 2xy - 5yz + 3yx - 7yz
h) 2a² + 3ab + a² - 2ba
i) 6 + 2mn - 5 + m + 3nm
j) 9k² - 8kt + 7t² + 8tk

Explanation:

Step1: Combine like - terms

For the expression \(2a - 4b+8a + 2b\), combine the \(a\) - terms and \(b\) - terms.
\((2a + 8a)+(-4b + 2b)=10a-2b\)

Step2: Combine like - terms for \(7x + 3y-3x + 4y\)

\((7x-3x)+(3y + 4y)=4x + 7y\)

Step3: Combine like - terms for \(9m-2n + 7n+2m\)

\((9m + 2m)+(-2n + 7n)=11m + 5n\)

Step4: Combine like - terms for \(9p-7 + 6p-5\)

\((9p+6p)+(-7-5)=15p-12\)

Step5: Combine like - terms for \(8r-10-5a + 2\)

\(-5a + 8r+(-10 + 2)=-5a + 8r-8\)

Step6: Combine like - terms for \(12-6p-5q + 3\)

\(-6p-5q+(12 + 3)=-6p-5q + 15\)

Step7: Combine like - terms for \(9k+6m-7k-4m\)

\((9k-7k)+(6m-4m)=2k + 2m\)

Step8: Combine like - terms for \(3m-5m+9k-7k\)

\((3m-5m)+(9k-7k)=-2m + 2k\)

Step9: Combine like - terms for \(x + 7y-5y+2x\)

\((x + 2x)+(7y-5y)=3x + 2y\)

Step10: Combine like - terms for \(10t+2w-11t-6w\)

\((10t-11t)+(2w-6w)=-t-4w\)

Step11: Combine like - terms for \(5ab-4bc + 2ab+3bc\)

\((5ab + 2ab)+(-4bc + 3bc)=7ab-bc\)

Step12: Combine like - terms for \(6mn-3m + 4mn-5m\)

\((6mn + 4mn)+(-3m-5m)=10mn-8m\)

Step13: Combine like - terms for \(6-4kl-9-5kl\)

\((-4kl-5kl)+(6-9)=-9kl-3\)

Step14: Combine like - terms for \(7x^{2}+6x-6x^{2}-9x\)

\((7x^{2}-6x^{2})+(6x-9x)=x^{2}-3x\)

Step15: Combine like - terms for \(9p-6q^{2}+5q^{2}-7q\)

\(-6q^{2}+5q^{2}+9p-7q=-q^{2}+9p-7q\)

Step16: Combine like - terms for \(7 + 4h-10h-16\)

\((4h-10h)+(7-16)=-6h-9\)

Step17: Combine like - terms for \(5xy-2yx\)

Since \(xy = yx\), \((5 - 2)xy=3xy\)

Step18: Combine like - terms for \(4ab-10ba + a\)

Since \(ab = ba\), \((4-10)ab + a=-6ab + a\)

Step19: Combine like - terms for \(-2mn+8nm + 6\)

Since \(mn=nm\), \((-2 + 8)mn+6 = 6mn+6\)

Step20: Combine like - terms for \(10-ab-5ab\)

\(-ab-5ab + 10=-6ab + 10\)

Step21: Combine like - terms for \(5m^{2}+7m + 3-2m^{2}-5m\)

\((5m^{2}-2m^{2})+(7m-5m)+3=3m^{2}+2m + 3\)

Step22: Combine like - terms for \(6a^{2}+9a-1 + 5a^{2}-10a\)

\((6a^{2}+5a^{2})+(9a-10a)-1=11a^{2}-a-1\)

Step23: Combine like - terms for \(2xy-5yz+3yx-7yz\)

Since \(xy = yx\), \((2xy+3yx)+(-5yz-7yz)=5xy-12yz\)

Step24: Combine like - terms for \(2a^{2}+3ab + a^{2}-2ba\)

Since \(ab = ba\), \((2a^{2}+a^{2})+(3ab-2ba)=3a^{2}+ab\)

Step25: Combine like - terms for \(6 + 2mn-5 + m+3nm\)

Since \(mn=nm\), \((2mn+3nm)+m+(6 - 5)=5mn+m + 1\)

Step26: Combine like - terms for \(9k^{2}-8kt+7t^{2}+8tk\)

Since \(kt = tk\), \(9k^{2}+7t^{2}+(-8kt + 8tk)=9k^{2}+7t^{2}\)

Answer:

a) \(10a - 2b\)
b) \(4x + 7y\)
c) \(11m+5n\)
d) \(15p - 12\)
e) \(-5a + 8r-8\)
f) \(-6p-5q + 15\)
g) \(2k + 2m\)
h) \(-2m + 2k\)
i) \(3x + 2y\)
j) \(-t-4w\)
k) \(7ab - bc\)
l) \(10mn-8m\)
m) \(-9kl-3\)
n) \(x^{2}-3x\)
o) \(-q^{2}+9p-7q\)
p) \(-6h-9\)
7a) \(3xy\)
7b) \(-6ab + a\)
7c) \(6mn+6\)
7d) \(-6ab + 10\)
7e) \(3m^{2}+2m + 3\)
7f) \(11a^{2}-a-1\)
7g) \(5xy-12yz\)
7h) \(3a^{2}+ab\)
7i) \(5mn+m + 1\)
7j) \(9k^{2}+7t^{2}\)