Math

QuestionMultiply the polynomials and combine like terms: (x+4)(x+3)(x+4)(x+3).

Studdy Solution

STEP 1

Assumptions1. We are multiplying two binomial expressions (x+4)(x+4) and (x+3)(x+3). We will use the distributive property to multiply these binomials3. Like terms will be combined in the final step

STEP 2

The distributive property states that for any real numbers a, b, and c, the equation (a+b)c=ac+bc(a+b)c = ac + bc holds true. We will apply this property to our binomials.

STEP 3

First, distribute the first term of the first binomial, xx, to both terms of the second binomial.
x(x+3)=x2+3xx(x+3) = x^2 +3x

STEP 4

Next, distribute the second term of the first binomial, 44, to both terms of the second binomial.
4(x+3)=4x+124(x+3) =4x +12

STEP 5

Now, we combine the results from steps3 and4.
x2+3x+4x+12x^2 +3x +4x +12

STEP 6

Finally, we combine like terms. The like terms in our equation are 3x3x and 4x4x.
x2+x+12x^2 +x +12The product of the binomials (x+4)(x+3)(x+4)(x+3) is x2+x+12x^2 +x +12.

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