Question

6 simplify
a) 2a + 4b + 8a + 2b
b) 7x + 3y − 3x + 4y
c) 9m − 2n + 7n + 2m
d) 9p − 7 + 6p − 5
e) 8a − 10 − 5a + 2
f) 12 − 6p − 5q + 3
g) 9k + 6n − 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: Simplify 6a) \(2a + 4b + 8a + 2b\)

Combine like terms: \((2a + 8a)+(4b + 2b)=10a + 6b\)

Step2: Simplify 6b) \(7x + 3y - 3x + 4y\)

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

Step3: Simplify 6c) \(9m - 2n + 7n + 2m\)

Combine like terms: \((9m + 2m)+(-2n + 7n)=11m + 5n\)

Step4: Simplify 6d) \(9p - 7 + 6p - 5\)

Combine like terms: \((9p + 6p)+(-7 - 5)=15p - 12\)

Step5: Simplify 6e) \(8a - 10 - 5a + 2\)

Combine like terms: \((8a - 5a)+(-10 + 2)=3a - 8\)

Step6: Simplify 6f) \(12 - 6p - 5q + 3\)

Combine like terms: \((12 + 3)-6p - 5q=15 - 6p - 5q\)

Step7: Simplify 6g) \(9k + 6n - 7k - 4n\)

Combine like terms: \((9k - 7k)+(6n - 4n)=2k + 2n\)

Step8: Simplify 6h) \(3m - 5m + 9k - 7k\)

Combine like terms: \((3m - 5m)+(9k - 7k)=-2m + 2k\)

Step9: Simplify 6i) \(x + 7y - 5y + 2x\)

Combine like terms: \((x + 2x)+(7y - 5y)=3x + 2y\)

Step10: Simplify 6j) \(10t + 2w - 11t - 6w\)

Combine like terms: \((10t - 11t)+(2w - 6w)=-t - 4w\)

Step11: Simplify 6k) \(5ab - 4bc + 2ab + 3bc\)

Combine like terms: \((5ab + 2ab)+(-4bc + 3bc)=7ab - bc\)

Step12: Simplify 6l) \(6mn - 3m + 4mn - 5m\)

Combine like terms: \((6mn + 4mn)+(-3m - 5m)=10mn - 8m\)

Step13: Simplify 6m) \(6 - 4kl - 9 - 5kl\)

Combine like terms: \((6 - 9)+(-4kl - 5kl)=-3 - 9kl\)

Step14: Simplify 6n) \(7x^2 + 6x - 6x^2 - 9x\)

Combine like terms: \((7x^2 - 6x^2)+(6x - 9x)=x^2 - 3x\)

Step15: Simplify 6o) \(9p - 6q^2 + 5q^2 - 7q\)

Combine like terms: \(9p+(-6q^2 + 5q^2)-7q=9p - q^2 - 7q\)

Step16: Simplify 6p) \(7 + 4h - 10h - 16\)

Combine like terms: \((7 - 16)+(4h - 10h)=-9 - 6h\)

Step17: Simplify 7a) \(5xy - 2yx\)

Since \(xy = yx\), combine like terms: \((5 - 2)xy = 3xy\)

Step18: Simplify 7b) \(4ab - 10ba + a\)

Since \(ab = ba\), combine like terms: \((4 - 10)ab + a=-6ab + a\)

Step19: Simplify 7c) \(-2mn + 8nm + 6\)

Since \(mn = nm\), combine like terms: \((-2 + 8)mn + 6=6mn + 6\)

Step20: Simplify 7d) \(10 - ab - 5ab\)

Combine like terms: \(10+(-1 - 5)ab=10 - 6ab\)

Step21: Simplify 7e) \(5m^2 + 7m + 3 - 2m^2 - 5m\)

Combine like terms: \((5m^2 - 2m^2)+(7m - 5m)+3=3m^2 + 2m + 3\)

Step22: Simplify 7f) \(6a^2 + 9a - 1 + 5a^2 - 10a\)

Combine like terms: \((6a^2 + 5a^2)+(9a - 10a)-1=11a^2 - a - 1\)

Step23: Simplify 7g) \(2xy - 5yz + 3yx - 7yz\)

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

Step24: Simplify 7h) \(2a^2 + 3ab + a^2 - 2ba\)

Since \(ab = ba\), combine like terms: \((2a^2 + a^2)+(3ab - 2ab)=3a^2 + ab\)

Step25: Simplify 7i) \(6 + 2mn - 5 + m + 3nm\)

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

Step26: Simplify 7j) \(9k^2 - 8kt + 7t^2 + 8tk\)

Since \(kt = tk\), combine like terms: \(9k^2+(-8kt + 8kt)+7t^2=9k^2 + 7t^2\)

Answer:

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