To FOIL (First, Outer, Inner, Last), we start by multiplying the first term in each grouping together:

$\displaystyle x \times x = x^2$

Then we multiply the outer terms together (the first term in the first grouping, the last term in the second grouping):

$\displaystyle x \times -7 = -7x$

Then we multiply the inner terms together (the second term in the first grouping, the first term in the second grouping):

$\displaystyle 4 \times x =4x$

And finally the last term in each grouping:

$\displaystyle 4 \times -7 = -28$

We can then collect everything back into our function:

$\displaystyle f(x)=x^2 - 7x + 4x - 28$

And combine like terms (in this case, both terms with an $\displaystyle x$ in them):

$\displaystyle f(x)= x^2-3x-28$

$\displaystyle (x+2)(x-9)$

This problem uses the distributive property. When using the distributive property on two sums, we apply the FOIL method. FOIL is an acronym that means, First, Outer, Inner, Last. This means we multiply the first term by the first term, the outer term by the outer term, the inner term by the inner term, and the last term by the last term. Take all of these products and add them together. To put this in a more general equation:

$\displaystyle (a+b)(c+d)=ac+ad+bc+bd$

Applying this formula to our problem we have,

$\displaystyle (x+2)(x-9)= (x*x)+(x*-9)+(2*x)+(2*-9)$

$\displaystyle (x+2)(x-9)= x^2-9x+2x-18$

$\displaystyle (x+2)(x-9)= x^2-7x-18$

And thus, our answer is

$\displaystyle x^2-7x-18$

Recall that FOIL means multiplying the first terms, then outside terms, next inside terms, and finally, the last terms:

$\displaystyle 8x^2+12x-2x-3$.

Then, combine like terms to get your answer of

$\displaystyle 8x^2+10x-3$.

Use the FOIL method to expand the binomials.

$\displaystyle (2x-8)(7x+6) = (2x)(7x)+(2x)(6)+(-8)(7x)+(-8)(6)$

Simplify the terms on the right side of the equal sign.

$\displaystyle 14x^2+12x-56x-48$

Combine like-terms.

The answer is:  $\displaystyle 14x^2-44x-48$

Use FOIL to multiply these binomials.

First multiply the first terms

$\displaystyle (2x\cdot 4x=8x^2)$,

then the outside terms

$\displaystyle (2x\cdot 3=6x)$,

next the inside terms

$\displaystyle (-1\cdot 4x=-4x)$,

and finally, the last terms

$\displaystyle (-1\cdot 3=-3)$.

That gives you

$\displaystyle 8x^2+6x-4x-3$.

Combine like terms to get your final answer of

$\displaystyle 8x^2+2x-3$.

Remember to use FOIL when multiplying.

Multiply the first terms

$\displaystyle (3x^2\cdot 4x=12x^3)$,

then the outside terms

$\displaystyle (3x^2\cdot 2=6x^2)$,

next the inside terms

$\displaystyle (-1\cdot 4x=-4x)$,

and finally, the last terms

$\displaystyle (-1\cdot 2=-2)$.

Put those all together to get your answer:

$\displaystyle 12x^3+6x^2-4x-2.$

Distribute the first term of the binomial with both terms of the second binomial.

$\displaystyle 2b^2(5b^2+b) = 10b^4+2b^3$

Distribute the second term of the binomial with both terms of the second binomial.

$\displaystyle (-3)(5b^2+b) = -15b^2-3b$

Add the terms together.

The answer is:  $\displaystyle 10b^4+2b^3 -15b^2-3b$

To multiply these two binomials, use FOIL.

Multiply the first terms

$\displaystyle (6x\cdot x=6x^2)$,

then the outside terms

$\displaystyle (6x\cdot 3=18x)$,

next the inside terms

$\displaystyle (-1\cdot x=-x)$,

and finally the last terms

$\displaystyle (-1\cdot 3=-3)$.

Put those all together to get:

$\displaystyle 6x^2+18x-x-3$.

Combine like terms to get your final answer of

$\displaystyle 6x^2+17x-3.$

Expand by using the FOIL method.

$\displaystyle (-2x^2-3)(-5x^2-4)$

$\displaystyle =(-2x^2)(-5x^2)+(-2x^2)(-4)+(-3)(-5x^2)+(-3)(-4)$

Simplify each term.

$\displaystyle 10x^4+8x^2+15x^2+12$

Combine like terms.

The answer is:  $\displaystyle 10x^4+23x^2+12$

Expand the expression by using the FOIL method.

$\displaystyle (3x-9)(4x-1)$

$\displaystyle = (3x)(4x)+(3x)(-1)+(-9)(4x)+(-9)(-1)$

Simplify all the terms.

$\displaystyle 12x^2-3x-36x+9$

Combine like-terms.

The answer is:  $\displaystyle 12x^2-39x+9$