Question

write the expression equivalent.

1. (6r - 7)(3r - 4)
2. (x - 7)(8x + 2)
3. (k + 4)(5k + 8)

Explanation:

Step1: Expand using FOIL method

For (6r-7)(3r-4):

Multiply first terms: $6r \times 3r = 18r^2$
Multiply outer terms: $6r \times (-4) = -24r$
Multiply inner terms: $-7 \times 3r = -21r$
Multiply last terms: $-7 \times (-4) = 28$
Combine terms: $18r^2 -24r -21r +28$

Step2: Combine like terms

$18r^2 + (-24r-21r) +28 = 18r^2 -45r +28$

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Step1: Expand using FOIL method

For (x-7)(8x+2):

Multiply first terms: $x \times 8x = 8x^2$
Multiply outer terms: $x \times 2 = 2x$
Multiply inner terms: $-7 \times 8x = -56x$
Multiply last terms: $-7 \times 2 = -14$
Combine terms: $8x^2 +2x -56x -14$

Step2: Combine like terms

$8x^2 + (2x-56x) -14 = 8x^2 -54x -14$

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Step1: Expand using FOIL method

For (k+4)(5k+8):

Multiply first terms: $k \times 5k = 5k^2$
Multiply outer terms: $k \times 8 = 8k$
Multiply inner terms: $4 \times 5k = 20k$
Multiply last terms: $4 \times 8 = 32$
Combine terms: $5k^2 +8k +20k +32$

Step2: Combine like terms

$5k^2 + (8k+20k) +32 = 5k^2 +28k +32$

Answer:

1. $18r^2 -45r +28$
2. $8x^2 -54x -14$
3. $5k^2 +28k +32$