ACT Math - How to use FOIL with exponents

Distribute and simplify:

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

$5x^2\cdot 2x = 10x^3$

Multiply the Outer terms:

$5x^2\cdot 1 = 5x^2$

Multiply the Inner terms:

$-x\cdot 2x = -2x^2$

Multiply the Last terms:

$-x\cdot 1 = -x$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms).

Arrange your answer in descending exponential form, and you're done.

The concept of FOIL can be applied to both an exponential expression and to an exponential modifier on an existing expression.

For all , = __________.

$9x^6 + 21x^{10} + 49x^4$

Explanation

Using FOIL, we see that $(3x^3 + 7x^2)^2 = (3x^3 + 7x^2) \cdot(3x^3 + 7x^2)$

First = $3x^3 \cdot 3x^3 = 9x^6$

Outer = $3x^3 \cdot 7x^2 = 21x^5$

Inner = $7x^2 \cdot 3x^3 = 21x^5$

Last = $7x^2 \cdot 7x^2 = 49x^4$

Remember that terms with like exponents are additive, so we can combine our middle terms:

Now order the expression from the highest exponent down:

Thus,

Use the FOIL method to simplify the following expression:

Explanation

Use the FOIL method to simplify the following expression:

Step 1: Expand the expression.

Step 2: FOIL

First: $x^3\cdot x^3 = x^6$

Outside: $x^3 \cdot 2x^2 =2x^5$

Inside: $2x^2 \cdot x^3 = 2x^5$

Last: $2x^2 \cdot 2x^2 = 4x^4$

Step 2: Sum the products.

Distribute and simplify:

$6x^{11} - 6x^{10} +12x^5 - 12x^4$

$7x^5 - 4x^{11} + x^{10} - 2x^5$

$12x^{25} + 6x^{18} - 4x^{10} - 12x^4$

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

$2x^4\cdot 6x = 12x^5$

Multiply the Outer terms:

$2x^4\cdot 3x^7 = 6x^{11}$

Multiply the Inner terms:

$-2x^3\cdot 6x = -12x^4$

Multiply the Last terms:

$-2x^3\cdot 3x^7 = -6x^{10}$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms). In this case, no two terms are compatible.

Arrange your answer in descending exponential form, and you're done.

$(2x^4-2x^3)(6x+3x^7) = 6x^{11} - 6x^{10} +12x^5 - 12x^4$

If , what is the value of the equation $q(q-7)^{2}$ ?

Explanation

Plug in for in the equation $q(q-7)^{2}$

That gives: $2(2-7)^{2}$

Then solve the computation inside the parenthesis: $2(-5)^{2}$

The answer should then be

$(4x-9)^{3}=?$

Explanation

FOIL the first two terms:

Next, multiply this expression by the last term:

Finally, combine the terms:

For all $x,\ (5x+2)^{2}=$ ?

$25x^{2}+20x+4$

$25x^{2}+10x+4$

$25x^{2}+4$

$10x+4$

$10x^{2}+4$

Explanation

$(5x+2)^{2}$ is equivalent to $(5x+2)(5x+2)$ .

Using the FOIL method, you multiply the first number of each set $5x\cdot 5x=25x^{2}$ , multiply the outer numbers of each set $5x\cdot 2=10x$ , multiply the inner numbers of each set $2\cdot 5x=10x$ , and multiply outer numbers of each set $2\cdot 2=4$ .