QuestionSimplify the expression: $-4 x(-3 y-7 z+2 x)+3 y(2 x+y)$ .

Studdy Solution

STEP 1

Assumptions1. The expression is $-4 x(-3 y-7 z+ x)+3 y( x+y)$ . We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute $-4x$ to each term in the parenthesis $(- y-7 z+2 x)$ .
$-4x(-y) -4x(-7z) -4x(2x)$

STEP 3

Next, simplify the multiplication.
$12xy +28xz -8x^2$

STEP 4

Now, distribute $3y$ to each term in the parenthesis $(2 x+y)$ .
$3y(2x) +3y(y)$

STEP 5

implify the multiplication.
$xy +3y^2$

STEP 6

Combine the terms from steps3 and5 to form the simplified expression.
$12xy +28xz -8x^2 +6xy +3y^2$

STEP 7

Combine like terms.
$12xy +6xy +28xz -x^2 +3y^2$

STEP 8

implify the expression.
$18xy +28xz -8x^2 +3y^2$ The simplified form of the expression is $18xy +28xz -8x^2 +3y^2$ .

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QuestionSimplify the expression: $-4 x(-3 y-7 z+2 x)+3 y(2 x+y)$ .

Studdy Solution

STEP 1

Assumptions1. The expression is $-4 x(-3 y-7 z+ x)+3 y( x+y)$ . We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute $-4x$ to each term in the parenthesis $(- y-7 z+2 x)$ .
$-4x(-y) -4x(-7z) -4x(2x)$

STEP 3

Next, simplify the multiplication.
$12xy +28xz -8x^2$

STEP 4

Now, distribute $3y$ to each term in the parenthesis $(2 x+y)$ .
$3y(2x) +3y(y)$

STEP 5

implify the multiplication.
$xy +3y^2$

STEP 6

Combine the terms from steps3 and5 to form the simplified expression.
$12xy +28xz -8x^2 +6xy +3y^2$

STEP 7

Combine like terms.
$12xy +6xy +28xz -x^2 +3y^2$

STEP 8

implify the expression.
$18xy +28xz -8x^2 +3y^2$ The simplified form of the expression is $18xy +28xz -8x^2 +3y^2$ .

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QuestionSimplify the expression: −4x(−3y−7z+2x)+3y(2x+y)-4 x(-3 y-7 z+2 x)+3 y(2 x+y)−4x(−3y−7z+2x)+3y(2x+y).

Studdy Solution

STEP 1

Assumptions1. The expression is −4x(−3y−7z+x)+3y(x+y)-4 x(-3 y-7 z+ x)+3 y( x+y)−4x(−3y−7z+x)+3y(x+y). We need to simplify the expression by distributing and combining like terms.

STEP 2

First, distribute −4x-4x−4x to each term in the parenthesis (−y−7z+2x)(- y-7 z+2 x)(−y−7z+2x).−4x(−y)−4x(−7z)−4x(2x)-4x(-y) -4x(-7z) -4x(2x)−4x(−y)−4x(−7z)−4x(2x)

STEP 3

Next, simplify the multiplication.12xy+28xz−8x212xy +28xz -8x^212xy+28xz−8x2

STEP 4

Now, distribute 3y3y3y to each term in the parenthesis (2x+y)(2 x+y)(2x+y).3y(2x)+3y(y)3y(2x) +3y(y)3y(2x)+3y(y)

STEP 5

implify the multiplication.xy+3y2xy +3y^2xy+3y2

STEP 6

Combine the terms from steps3 and5 to form the simplified expression.12xy+28xz−8x2+6xy+3y212xy +28xz -8x^2 +6xy +3y^212xy+28xz−8x2+6xy+3y2

STEP 7

Combine like terms.12xy+6xy+28xz−x2+3y212xy +6xy +28xz -x^2 +3y^212xy+6xy+28xz−x2+3y2

STEP 8

implify the expression.18xy+28xz−8x2+3y218xy +28xz -8x^2 +3y^218xy+28xz−8x2+3y2The simplified form of the expression is 18xy+28xz−8x2+3y218xy +28xz -8x^2 +3y^218xy+28xz−8x2+3y2.

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QuestionSimplify the expression: $-4 x(-3 y-7 z+2 x)+3 y(2 x+y)$ .

Assumptions1. The expression is $-4 x(-3 y-7 z+ x)+3 y( x+y)$ . We need to simplify the expression by distributing and combining like terms.

First, distribute $-4x$ to each term in the parenthesis $(- y-7 z+2 x)$ .
$-4x(-y) -4x(-7z) -4x(2x)$

Next, simplify the multiplication.
$12xy +28xz -8x^2$

Now, distribute $3y$ to each term in the parenthesis $(2 x+y)$ .
$3y(2x) +3y(y)$

implify the multiplication.
$xy +3y^2$

Combine the terms from steps3 and5 to form the simplified expression.
$12xy +28xz -8x^2 +6xy +3y^2$

Combine like terms.
$12xy +6xy +28xz -x^2 +3y^2$

implify the expression.
$18xy +28xz -8x^2 +3y^2$ The simplified form of the expression is $18xy +28xz -8x^2 +3y^2$ .