Question

Drag the tiles to the correct boxes to complete the pairs.

Match each expression to its equivalent form.
Tiles
(x + 4)(x − 4)
(x + 2y)(x2 − 2xy + 4y2)
4x2 + 12xy + 9y2
8x3 + 12x2 + 6x + 1
Pairs
x2 − 16

(2x + 1)3

(2x + 3y)2

x3 + 8y3

Answer 1

Answer:

1. A

2. D

3. C

4. B

Step-by-step explanation:

Use formulas:

$a^2-b^2=(a+b)(a-b)\\ \\a^3+b^3=(a+b)(a^2-ab+b^2)\\ \\(a+b)^2=a^2+2ab+b^2\\ \\(a+b)^3=a^3+3a^2b+3ab^2+b^3$

Then

$x^2-16=x^2-4^2=(x+4)(x-4)\\ \\(2x+1)^3=(2x)^3+3\cdot (2x)^2\cdot 1+3\cdot (2x)\cdot 1^2+1^3=8x^3+12x^2+6x+1\\ \\(2x+3y)^2=(2x)^2+2\cdot (2x)\cdot (3y)+(3y)^2=4x^2+12xy+9y^2\\ \\x^3+8y^3=x^3+(2y)^3=(x+2y)(x^2-x\cdot (2y)+(2y)^2)=(x+2y)(x^2-2xy+4y^2)$