Multiplying polynomials worksheet with binomial multiplication examples and practice problems.

Here are the step-by-step solutions for the problems on your worksheet.

MULTIPLYING BINOMIALS

1. $(x - 4)(x + 10)$
* Multiply First terms: $x \cdot x = x^2$
* Multiply Outer terms: $x \cdot 10 = 10x$
* Multiply Inner terms: $-4 \cdot x = -4x$
* Multiply Last terms: $-4 \cdot 10 = -40$
* Combine like terms ($10x - 4x = 6x$):
Answer: $x^2 + 6x - 40$

2. $(x + 5)(x - 9)$
* Multiply First terms: $x \cdot x = x^2$
* Multiply Outer terms: $x \cdot -9 = -9x$
* Multiply Inner terms: $5 \cdot x = 5x$
* Multiply Last terms: $5 \cdot -9 = -45$
* Combine like terms ($-9x + 5x = -4x$):
Answer: $x^2 - 4x - 45$

3. $(2x - 4)(3x + 6)$
* Multiply First terms: $2x \cdot 3x = 6x^2$
* Multiply Outer terms: $2x \cdot 6 = 12x$
* Multiply Inner terms: $-4 \cdot 3x = -12x$
* Multiply Last terms: $-4 \cdot 6 = -24$
* Combine like terms ($12x - 12x = 0$):
Answer: $6x^2 - 24$

4. $(5x - 7y)(-x + 8y)$
* Multiply First terms: $5x \cdot -x = -5x^2$
* Multiply Outer terms: $5x \cdot 8y = 40xy$
* Multiply Inner terms: $-7y \cdot -x = 7xy$ (negative times negative is positive)
* Multiply Last terms: $-7y \cdot 8y = -56y^2$
* Combine like terms ($40xy + 7xy = 47xy$):
Answer: $-5x^2 + 47xy - 56y^2$

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YOU TRY:

1. $(x - 7)(x - 1)$
* Multiply First terms: $x \cdot x = x^2$
* Multiply Outer terms: $x \cdot -1 = -1x$
* Multiply Inner terms: $-7 \cdot x = -7x$
* Multiply Last terms: $-7 \cdot -1 = 7$
* Combine like terms ($-1x - 7x = -8x$):
Answer: $x^2 - 8x + 7$

2. $(3x + 5)(2x - 8)$
* Multiply First terms: $3x \cdot 2x = 6x^2$
* Multiply Outer terms: $3x \cdot -8 = -24x$
* Multiply Inner terms: $5 \cdot 2x = 10x$
* Multiply Last terms: $5 \cdot -8 = -40$
* Combine like terms ($-24x + 10x = -14x$):
Answer: $6x^2 - 14x - 40$

3. $(x - 4y)^2$
* Rewrite as $(x - 4y)(x - 4y)$
* Multiply First terms: $x \cdot x = x^2$
* Multiply Outer terms: $x \cdot -4y = -4xy$
* Multiply Inner terms: $-4y \cdot x = -4xy$
* Multiply Last terms: $-4y \cdot -4y = 16y^2$
* Combine like terms ($-4xy - 4xy = -8xy$):
Answer: $x^2 - 8xy + 16y^2$

4. $(2x + 8y)(-7x - 3y)$
* Multiply First terms: $2x \cdot -7x = -14x^2$
* Multiply Outer terms: $2x \cdot -3y = -6xy$
* Multiply Inner terms: $8y \cdot -7x = -56xy$
* Multiply Last terms: $8y \cdot -3y = -24y^2$
* Combine like terms ($-6xy - 56xy = -62xy$):
Answer: $-14x^2 - 62xy - 24y^2$

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Final Answer:
Multiplying Binomials:
1. $x^2 + 6x - 40$
2. $x^2 - 4x - 45$
3. $6x^2 - 24$
4. $-5x^2 + 47xy - 56y^2$

You Try:
1. $x^2 - 8x + 7$
2. $6x^2 - 14x - 40$
3. $x^2 - 8xy + 16y^2$
4. $-14x^2 - 62xy - 24y^2$