Using the foil method multiply (x2-7)(x2-4) then add any like terms and write polynomial in standard form. Show your work. Any body good at this ? I hope so, I can’t figure them out! :((

  x^4 -11x^2 +28

Step-by-step explanation:

The FOIL method tells you to form the products of ...

  First terms: (x^2)(x^2) = x^4

  Outer terms: (x^2)(-4) = -4x^2 . . . . first term of first factor × last term of last factor

  Inner terms: (-7)(x^2) = -7x^2 . . . . terms next to the adjacent parentheses

  Last terms: (-7)(-4) = 28 . . . . . . . . . second term of each binomial

The only terms that need to be combined are the Outer and Inner terms. In this product, their sum is ...

  -4x^2 -7x^2 = -11x^2

Then the product is x^4 -11x^2 +28.

Apart from your multiplication tables (or use of your calculator), you only need to know how to find the exponent of the product of powers of x. That result is the sum of the exponents of the factors:

  (x^a)(x^b) = x^(a+b)

  (x^2)(x^2) = x^(2+2) = x^4

Comment on FOIL

The term FOIL is intended to be a mnemonic to remind you how to multiply two binomials. The method only works with two binomials.

The more general case is the use of the distributive property, which is needed for multiplying sums that are not binomials.

Using the distributive property gets you the same place in the end:

  (x^2 -7)(x^2 -4) = x^2(x^2 -4) -7(x^2 -4) . . . . . second factor multiplies each term of the first factor

Now you can go the next step to distribute the outside factor to all the inside terms:

  = (x^2)(x^2) +(x^2)(-4) -7(x^2) -7(-4)

  = x^4 -4x^2 -7x^2 +28 . . . . . . . same terms as FOIL, above

  = x^4 -11x^2 +28 . . . . . . . . . . . . same product as above

step-by-step explanation:

wrgasadvauoyfaiua-00uhf

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.