Can anyone help me with these questions? Please
1. ac - bc + ad - bd
2. xy - 3x - 8y + 24
3. 4x^2 + 20x + 5y +xy
4. 48x^2y + 20xz +12xy + 5z
Do some grouping and factoring. For instance, the first..
ac - bc + ad - bd
(a-b)c + (a-b)d
(a-b)(c+d)
Sure, I can help you with those questions!
1. To simplify the expression ac - bc + ad - bd, you can group the terms with common factors. In this case, we notice that each term has a common factor of (a - b):
ac - bc + ad - bd
= (a - b)c + (a - b)d
Now, we can factor out (a - b) from both terms:
(a - b)c + (a - b)d
= (a - b)(c + d)
So, the simplified expression is (a - b)(c + d).
2. Let's simplify the expression xy - 3x - 8y + 24 by grouping the terms:
xy - 3x - 8y + 24
= (xy - 3x) + (-8y + 24)
Now, let's factor out common factors from each group:
(xy - 3x) + (-8y + 24)
= x(y - 3) - 8(y - 3)
As we can see, both terms have a common factor of (y - 3). Now, we can factor it out:
x(y - 3) - 8(y - 3)
= (y - 3)(x - 8)
So, the simplified expression is (y - 3)(x - 8).
3. For the expression 4x^2 + 20x + 5y + xy, we can factor it by grouping the terms:
4x^2 + 20x + 5y + xy
= (4x^2 + 20x) + (5y + xy)
Now, let's factor out common factors from each group:
(4x^2 + 20x) + (5y + xy)
= 4x(x + 5) + y(5 + x)
The terms (x + 5) and (5 + x) are equivalent expressions, so we can simplify it further:
4x(x + 5) + y(5 + x)
= 4x(x + 5) + y(x + 5)
Now, we notice that both terms have a common factor of (x + 5). We can factor it out:
4x(x + 5) + y(x + 5)
= (x + 5)(4x + y)
So, the simplified expression is (x + 5)(4x + y).
4. Let's simplify the expression 48x^2y + 20xz +12xy + 5z by grouping the terms:
48x^2y + 20xz + 12xy + 5z
= (48x^2y + 12xy) + (20xz + 5z)
Now, let's factor out common factors from each group:
(48x^2y + 12xy) + (20xz + 5z)
= 12xy(4x + 1) + 5z(4x + 1)
Now, we see that both terms have a common factor of (4x + 1). We can factor it out:
12xy(4x + 1) + 5z(4x + 1)
= (4x + 1)(12xy + 5z)
So, the simplified expression is (4x + 1)(12xy + 5z).
By grouping the terms and factoring out common factors, we are able to simplify the given expressions.