Question

multiply binomials
1 ( 3x−5 )( x+1 )
answer:
2 ( 2x−3 )( x+3 )
answer:
3 ( 3x−2 )( x - 2 )
answer:
4 ( 5x+4 )( x+3 )
answer:
5 ( 2x+1 )( x+5 )
answer:
6 ( 2x+1 )( x+2 )
answer:

Explanation:

Step1: Multiply using FOIL method

For $(3x-5)(x+1)$:
First terms: $3x \cdot x = 3x^2$
Outer terms: $3x \cdot 1 = 3x$
Inner terms: $-5 \cdot x = -5x$
Last terms: $-5 \cdot 1 = -5$
Combine like terms: $3x^2 + 3x -5x -5 = 3x^2 -2x -5$

Step2: Multiply using FOIL method

For $(2x-3)(x+3)$:
First terms: $2x \cdot x = 2x^2$
Outer terms: $2x \cdot 3 = 6x$
Inner terms: $-3 \cdot x = -3x$
Last terms: $-3 \cdot 3 = -9$
Combine like terms: $2x^2 +6x -3x -9 = 2x^2 +3x -9$

Step3: Multiply using FOIL method

For $(3x-2)(x-2)$:
First terms: $3x \cdot x = 3x^2$
Outer terms: $3x \cdot (-2) = -6x$
Inner terms: $-2 \cdot x = -2x$
Last terms: $-2 \cdot (-2) = 4$
Combine like terms: $3x^2 -6x -2x +4 = 3x^2 -8x +4$

Step4: Multiply using FOIL method

For $(5x+4)(x+3)$:
First terms: $5x \cdot x = 5x^2$
Outer terms: $5x \cdot 3 = 15x$
Inner terms: $4 \cdot x = 4x$
Last terms: $4 \cdot 3 = 12$
Combine like terms: $5x^2 +15x +4x +12 = 5x^2 +19x +12$

Step5: Multiply using FOIL method

For $(2x+1)(x+5)$:
First terms: $2x \cdot x = 2x^2$
Outer terms: $2x \cdot 5 = 10x$
Inner terms: $1 \cdot x = x$
Last terms: $1 \cdot 5 = 5$
Combine like terms: $2x^2 +10x +x +5 = 2x^2 +11x +5$

Step6: Multiply using FOIL method

For $(2x+1)(x+2)$:
First terms: $2x \cdot x = 2x^2$
Outer terms: $2x \cdot 2 = 4x$
Inner terms: $1 \cdot x = x$
Last terms: $1 \cdot 2 = 2$
Combine like terms: $2x^2 +4x +x +2 = 2x^2 +5x +2$

Answer:

1. $3x^2 - 2x - 5$
2. $2x^2 + 3x - 9$
3. $3x^2 - 8x + 4$
4. $5x^2 + 19x + 12$
5. $2x^2 + 11x + 5$
6. $2x^2 + 5x + 2$

*(Note: For each box method grid, fill the cells as follows:

1. Top-left: $3x^2$, Top-right: $3x$, Bottom-left: $-5x$, Bottom-right: $-5$
2. Top-left: $2x^2$, Top-right: $6x$, Bottom-left: $-3x$, Bottom-right: $-9$
3. Top-left: $3x^2$, Top-right: $-6x$, Bottom-left: $-2x$, Bottom-right: $4$
4. Top-left: $5x^2$, Top-right: $15x$, Bottom-left: $4x$, Bottom-right: $12$
5. Top-left: $2x^2$, Top-right: $10x$, Bottom-left: $x$, Bottom-right: $5$
6. Top-left: $2x^2$, Top-right: $4x$, Bottom-left: $x$, Bottom-right: $2$)*