Multiply the polynomials by using FOIL.(5xy+3)(4xy−2)(5xy+3)(4xy-2)

20 x 2 y 2 + 2 x y − 6 20x^2y^2+2xy-6

Multiply the polynomials by using FOIL. ( 5 x y + 3 ) ( 4 x y − 2 ) (5xy+3)(4xy-2)

Here we're going to use our foil technique to combine these two binomials. We have five x y plus three times four x y minus two. So first we're going to multiply the first terms of each binomial to get five x y times four x y. Then we'll multiply our outside terms to get plus five x y times negative two. Then we'll multiply our inside terms to get plus three times four x y and finally our last terms to get plus three times negative two. And now we'll combine all of our like factors. So for our first term, we have five and four, which combine to make 20. We also have an x times x, which combines to make x squared. And we have y times y, which makes y squared. For our second term, we have five and negative two, which combine to make minus 10. And we have x and y, which don't have any like factors, so those will stay x times y. For our third term, we have three and four, which combine to make plus 12, also times x y. And for our last term, we have three and negative two, which combine to make negative six. Now here we want to check if we have any more terms in common. X squared and y squared doesn't have any terms in common, but negative 10 xy and 12 xy do have the variables x times y in common. So that means we can combine these two terms. So simplifying further, we'll have our 20 x squared y squared and negative 10 x y plus 12 x y makes positive two x y. So we have plus two x y minus six and this is our binomials now expanded out and simplified.

Multiply the polynomials by using FOIL. ( 5 x y + 3 ) ( 4 x y − 2 ) (5xy+3)(4xy-2)

20 x 2 y 2 + 2 x y − 6 20x^2y^2+2xy-6

20 x 2 y 2 − 2 x y − 6 20x^2y^2-2xy-6

20 x 2 y 2 + 6 x y − 6 20x^2y^2+6xy-6

20 x 2 y 2 − 6 x y − 6 20x^2y^2-6xy-6 20 x 2 y 2 − 6 x y − 6

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

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Multiple Choice

Multiply the polynomials by using FOIL.
$(5 x y + 3) (4 x y - 2)$

$20 x^{2} y^{2} - 2 x y - 6$

$20 x^{2} y^{2} + 6 x y - 6$

$20 x^{2} y^{2} + 2 x y - 6$

$20x^2y^2-6xy-6$

Verified step by step guidance

Identify the two binomials to multiply: $(5xy + 3)$ and $(4xy - 2)$.

Apply the FOIL method, which stands for First, Outer, Inner, Last, to multiply each pair of terms:

First: Multiply the first terms in each binomial: $5xy \times 4xy$.

Outer: Multiply the outer terms: $5xy \times (-2)$.

Inner: Multiply the inner terms: $3 \times 4xy$.

Last: Multiply the last terms in each binomial: $3 \times (-2)$.

Combine all these products into one expression: $(5xy \times 4xy) + (5xy \times -2) + (3 \times 4xy) + (3 \times -2)$.

Simplify each term by multiplying coefficients and variables (remember to add exponents when multiplying like bases): for example, $5xy \times 4xy = 20x^{2}y^{2}$.

Combine like terms, especially the terms involving $xy$, to write the expression in its simplest form.

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