## 19.1: Number Talk: Parentheses

Find the value of each expression mentally.

$2 + 3 \boldcdot 4$

$(2+3)(4)$

$2 - 3 \boldcdot 4$

Let's use the distributive property to write expressions in different ways.

Find the value of each expression mentally.

$2 + 3 \boldcdot 4$

$(2+3)(4)$

$2 - 3 \boldcdot 4$

$2 - (3 + 4)$

In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.

factored | expanded | |
---|---|---|

row 1 | $\text- 3(5 - 2y)$ | $\text- 15 + 6y$ |

row 2 | $5(a-6)$ | |

row 3 | $6a-2b$ | |

row 4 | $\text- 4(2w-5z)$ | |

row 5 | $\text- (2x-3y)$ | |

row 6 | $20x-10y+15z$ | |

row 7 | $k(4-17)$ | |

row 8 | $10a-13a$ | |

row 9 | $\text- 2x(3y-z)$ | |

row 10 | $ab-bc-3bd$ | |

row 11 | $\text- x(3y-z+4w)$ |

We can use properties of operations in different ways to rewrite expressions and create equivalent expressions. We have already seen that we can use the distributive property to expand an expression, for example $3(x+5) = 3x+15$. We can also use the distributive property in the other direction and factor an expression, for example $8x+12 = 4(2x+3)$.

We can organize the work of using distributive property to rewrite the expression $12x-8$. In this case we know the product and need to find the factors.

The terms of the product go inside:

*what* is 12$x$?" "4 times *what* is -8?" and write the other factors on the other side of the rectangle:

So, $12x-8$ is equivalent to $4(3x-2)$.