Question

find each product.

1. (7m + 8)(4m - 2)
2. (2b + 7)(5b - 8)
3. (7a - 7)(4a + 3)
4. (3x - 5y)(4x + 4y)
5. (-6x + 3y)(-4x - 2y)
6. (-m + n)(-m + 4n)

Explanation:

Step1: Use FOIL method for (7m + 8)(4m - 2)

\[

$$\begin{align*} &(7m\times4m)+(7m\times(- 2))+(8\times4m)+(8\times(-2))\\ =&28m^{2}-14m + 32m-16\\ =&28m^{2}+18m - 16 \end{align*}$$

\]

Step2: Use FOIL method for (2b + 7)(5b - 8)

\[

$$\begin{align*} &(2b\times5b)+(2b\times(-8))+(7\times5b)+(7\times(-8))\\ =&10b^{2}-16b+35b - 56\\ =&10b^{2}+19b - 56 \end{align*}$$

\]

Step3: Use FOIL method for (7a - 7)(4a + 3)

\[

$$\begin{align*} &(7a\times4a)+(7a\times3)+(-7\times4a)+(-7\times3)\\ =&28a^{2}+21a-28a - 21\\ =&28a^{2}-7a - 21 \end{align*}$$

\]

Step4: Use FOIL method for (3x - 5y)(4x + 4y)

\[

$$\begin{align*} &(3x\times4x)+(3x\times4y)+(-5y\times4x)+(-5y\times4y)\\ =&12x^{2}+12xy-20xy - 20y^{2}\\ =&12x^{2}-8xy - 20y^{2} \end{align*}$$

\]

Step5: Use FOIL method for (-6x + 3y)(-4x - 2y)

\[

$$\begin{align*} &(-6x\times(-4x))+(-6x\times(-2y))+(3y\times(-4x))+(3y\times(-2y))\\ =&24x^{2}+12xy-12xy - 6y^{2}\\ =&24x^{2}-6y^{2} \end{align*}$$

\]

Step6: Use FOIL method for (-m + n)(-m + 4n)

\[

$$\begin{align*} &(-m\times(-m))+(-m\times4n)+(n\times(-m))+(n\times4n)\\ =&m^{2}-4mn - mn+4n^{2}\\ =&m^{2}-5mn + 4n^{2} \end{align*}$$

\]

Answer:

1. $28m^{2}+18m - 16$
2. $10b^{2}+19b - 56$
3. $28a^{2}-7a - 21$
4. $12x^{2}-8xy - 20y^{2}$
5. $24x^{2}-6y^{2}$
6. $m^{2}-5mn + 4n^{2}$