Step-by-step explanation:
Note: I'm only providing solutions for Problem 9.
<h2>9. Simplify the following by collecting like terms:
</h2>
Combining like terms involve performing the required mathematical operations (using the PEMDAS rule). The terms must have the same degree (or exponents).
<h3>a) 3a + 7a </h3>
Add the coefficients of both terms.
3a + 7a = 10a
<h3>
</h3><h3>b) 4n + 3n
</h3>
Add the coefficients of both terms.
4n + 3n = 7n
<h3>
</h3><h3>c) 12y - 4y
</h3>
Subtract the coefficient of both terms.
12y - 4y = 8y
<h3>
</h3><h3>d) 5x + 2x + 4x
</h3>
Add the coefficients of all terms.
5x + 2x + 4x = 11x
<h3 /><h3>e) 6ab - 2ab - ba
</h3>
The last term, "ba," can be rewritten as, "ab." Remember that with algebraic expressions such as "ab," it essentially involves multiplication of both variables within the same term. Thus, ab = a × b. The variables ab also have a numerical coefficient of 1: 1a × 1b.
Now, we can perform the subtraction on all terms:
6ab - 2ab - ab = 3ab.
<h3 /><h3>f) 7mn + 2mn - 2mn
</h3>
Subtract 2mn from 2mn, which leaves you with 7mn:
7mn + 2mn - 2mn = 7mn
<h3 /><h3>g) 4y - 3y + 8
</h3>
For this algebraic expression, you could only combine the terms with the same variable and degree. Therefore, you'll have to subtract 3y from 4y, leaving the constant, 8, unaffected.
4y - 3y + 8 = y + 8
<h3>h) 7x + 5 - 4x
</h3>
Similar to question g, only combine the terms with the same degree and variable, leaving the constant unaffected.
7x + 5 - 4x = 3x + 5
<h3>i) 6xy + xy + 4y
</h3>
You could only combine the terms with the same set of variables and degree, which are the first two terms on this given question. You cannot combine the last term, 4y, into the other terms.
6xy + xy + 4y = 7xy + 4y
<h3>j) 5ab + 3 + 7ba
</h3>
Using the same reasoning as in question e: the last term, 7ba, can be rewritten as 7ab, for which you could combine with the first term, 5ab.
5ab + 3 + 7ba = 12ab + 3
<h3 /><h3>k) 2 - 5m - m </h3>
Combine the like terms, which are the second and the last term.
2 - 5m - m = 2 - 6m
<h3>l) 4 - 2x + x
</h3>
Combine the like terms, which are the second and the last term.
4 - 2x + x = 4 - x
