How do you factor this question? I don't understand
8p^2+40pq+50q^2
(2p + 5q)(4p + 10q)
8 p² + 40 p ∙ q + 50 q² =
2 ∙ 4 p² + 2 ∙ 20 p ∙ q + 2 ∙ 25 q² =
2 ∙ ( 4 p² + 20 p ∙ q + 25 q² ) =
2 ∙ ( 4 p² + 10 p ∙ q + 10 p ∙ q + 25 q² ) =
2 ∙ [ ( 4 p² + 10 p ∙ q ) + ( 10 p ∙ q + 25 q² ) ] =
2 ∙ [ ( 2 ∙ 2 ∙ p² + 2 ∙ 5 ∙ p ∙ q ) + ( 5 ∙ 2 p ∙ q + 5 ∙ 5 q² ) ] =
2 ∙ [ 2 p ∙ ( 2 p + 5 q ) + 5 q ∙ ( 2 p + 5 q ) ] =
2 ∙ [ ( 2 p + 5 q ) ∙ 2 p + ( 2 p + 5 q ) ∙ 5 q ] =
2 ∙ ( 2 p + 5 q ) ∙ ( 2 p + 5 q ) = 2 ∙ ( 2 p + 5 q )²
To factor the expression 8p^2 + 40pq + 50q^2, we look for common factors and then use the distributive property to break down the expression.
Step 1: Identify any common factors.
In this case, the coefficients 8, 40, and 50 have a common factor of 2. Also, the variables p and q do not have any common factors.
Step 2: Factor out the common factor.
Factoring out 2 from each term gives us:
2(4p^2 + 20pq + 25q^2)
Step 3: Factor the quadratic expression within the parentheses.
The expression 4p^2 + 20pq + 25q^2 is a quadratic trinomial, which can be factored as the square of a binomial.
First, find the square root of the first term (4p^2), which is 2p.
Next, find the square root of the last term (25q^2), which is 5q.
Now, the middle term is 20pq, which can be obtained by multiplying the square roots of the first and last terms (2p * 5q).
So, we can write the expression as:
2(2p + 5q)(2p + 5q)
Step 4: Simplify the expression.
Finally, since we have the same binomial term (2p + 5q) repeated twice, we can write it as the product of the binomial squared:
2(2p + 5q)^2
Therefore, the fully factored form of the expression 8p^2 + 40pq + 50q^2 is 2(2p + 5q)^2.