Math  /  Algebra

Question17. Complète la pyramide d'additions. Pour trouver la valeur à écrire dans une case, additionne les expressions qui sont dans les deux cases situées juste en dessous.

Studdy Solution

STEP 1

What is this asking? We need to fill in a pyramid where each block is the sum of the two blocks below it! Watch out! Don't forget to combine like terms carefully!

STEP 2

1. Sum the first two bottom expressions
2. Sum the other two bottom expressions
3. Sum the results of the previous two steps
4. Celebrate!

STEP 3

Let's **add** the first two expressions at the bottom: (2x1)(2x - 1) and (x+3)(x + 3).
Remember, we're doing this because each block is the sum of the two blocks directly beneath it!

STEP 4

(2x1)+(x+3)=2x+x1+3=3x+2(2x - 1) + (x + 3) = 2x + x - 1 + 3 = 3x + 2 So, the **sum** of the first two bottom expressions is 3x+23x + 2!

STEP 5

Now, let's **add** the other two expressions at the bottom: (3x2)(3x - 2) and (x+2)(x + 2).
We're doing this for the same reason as before: to build our pyramid up, block by block!

STEP 6

(3x2)+(x+2)=3x+x2+2=4x(3x - 2) + (x + 2) = 3x + x - 2 + 2 = 4x Awesome! The **sum** of the second pair is 4x4x!

STEP 7

We've found the values for the second level of our pyramid: 3x+23x + 2 and 4x4x.
Now, we just need to **add** these together to find the value for the top block!

STEP 8

(3x+2)+(4x)=3x+4x+2=7x+2(3x + 2) + (4x) = 3x + 4x + 2 = 7x + 2 The **top** of our pyramid is 7x+27x + 2!

STEP 9

The completed pyramid has 2x12x - 1, x+3x + 3, 3x23x - 2, and x+2x + 2 on the bottom row, 3x+23x + 2 and 4x4x on the second row, and 7x+27x + 2 at the top!

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