finding the product for (7x+1)(x^2+1) and for the problem (2x+6)(x-10) Also finding the product thank you very much
It is importnt that you attempt these problems yourself. use the rule that
(a+b)(c+d) = a(c+d) + b(c+d)
=ac + ad + bc + bd.
In other words, add up all the possible pairs of products from each of the two terms in parentheses.
In the first case, the answer is
7x^3 + 7x + x^2 + 1
Now you try the other one.
Use the rule:
X(A + B) = X A + X B
If you take:
X = (7x+1),
A = x^2 and
B = 1,
you get:
(7x+1)(x^2 + 1) = (7x+1)x^2 + (7x+1)1 =
x^2 (7x+1) + 7x+1
You can now expand the term x^2 (7x+1)
by using the same rule again. So you put:
X = x^2,
A = 7 x,
B = 1
To find the product of two binomial expressions, we can use the distributive property.
Let's start with the first problem: (7x + 1)(x^2 + 1).
Step 1: Apply the distributive property by multiplying the first term of the first expression by each term in the second expression, and then multiply the second term of the first expression by each term in the second expression.
(7x * x^2) + (7x * 1) + (1 * x^2) + (1 * 1)
Simplified: 7x^3 + 7x + x^2 + 1
So, the product of (7x + 1)(x^2 + 1) is 7x^3 + x^2 + 7x + 1.
Now let's move onto the second problem: (2x + 6)(x - 10).
Step 1: Apply the distributive property in the same way as before.
(2x * x) + (2x * -10) + (6 * x) + (6 * -10)
Simplified: 2x^2 - 20x + 6x - 60
Step 2: Combine like terms.
2x^2 - 14x - 60
So, the product of (2x + 6)(x - 10) is 2x^2 - 14x - 60.