Math

QuestionFactor the expression 25(x+7)210025(x+7)^{2}-100.

Studdy Solution

STEP 1

Assumptions1. We are asked to factor the equation 25(x+7)10025(x+7)^{}-100. . We are assuming that the equation is equal to zero.

STEP 2

The given equation is in the form of a2b2a^2 - b^2, which is a difference of squares. The difference of squares can be factored using the formula a2b2=(ab)(a+b)a^2 - b^2 = (a-b)(a+b).

STEP 3

Identify aa and bb in the given equation. Here, a=5(x+7)a =5(x+7) and b=10b =10.

STEP 4

Substitute aa and bb into the difference of squares formula.
(ab)(a+b)=((x+7)10)((x+7)+10)(a-b)(a+b) = ((x+7)-10)((x+7)+10)

STEP 5

implify the expressions in the parentheses.
(5x+3510)(5x+35+10)(5x+35-10)(5x+35+10)

STEP 6

implify further to get the factored form of the equation.
(5x+25)(5x+45)(5x+25)(5x+45)So, the factored form of the equation 25(x+)210025(x+)^{2}-100 is (5x+25)(5x+45)(5x+25)(5x+45).

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